Roots Definition and 978 Threads

  1. V

    Roots of a third degree polynomial

    Homework Statement Knowing that the equation: X^n-px^2=q^m has three positive real roots a, b and c. Then what is log_q[abc(a^2+b^2+c^2)^{a+b+c}] equal to? Homework Equations a + b + c = -(coefficient \ of \ second \ highest \ degree \ term) = -k_2 abc = -(constant \ coefficient) =...
  2. Jameson

    MHB Finding roots of a quadratic (Lindsay's question from Facebook)

    Lindsay on Facebook writes: I think you mean you got -48 instead of 48, but either way let's go through solving this. x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} Looking at $3x^2+12x+8$ we see that $a=3$, $b=12$ and $c=8$. Plugging that into the above quadratic equation yields. x = \frac{-12 \pm...
  3. B

    Finding Solutions for z in z^2 = a + bi

    Homework Statement z^2 = a + bi a = real number b = real number find all the solutions for z Homework Equations The Attempt at a Solution (x+y)^2 = a + bi ?
  4. U

    Roots lying between the roots of a given equation

    Homework Statement For what real values of 'a' do the roots of the equation x^2-2x-(a^2-1)=0 lie between the roots of the equation x^2-2(a+1)x+a(a-1)=0 Homework Equations The Attempt at a Solution The required conditions are \large D_1\geq0 \large D_2\geq0 \large...
  5. U

    Find the values of a for real and distinct roots

    Homework Statement Find the values of 'a' so that two of the roots of the equation (a-1)(x^2+x+1)^2=(a+1)(x^4+x^2+1) are real and distinct Homework Equations The Attempt at a Solution I am thinking of converting this equation in quadratic form so that I can find discriminant and make it...
  6. D

    MHB What are the roots of this polynomial with a beta coefficient?

    $\beta m^5 + m^2 + 1 =0$ How do I find the roots?
  7. V

    Roots of a fourth degree polynomial

    Homework Statement z^4 - z^2 + 1 = 0 is an equation in ℂ. Which of the following alternatives is the sum of two roots of this equation: (i) 2√3; (ii) -(√3)/2; (iii) (√3)/2; (iv) -i; (v) i/2 Homework EquationsThe Attempt at a Solution All I know is that the sum of all roots should equal 0...
  8. A

    Are there primitive roots in Z_32?

    What are the primitive roots of Z_32? \varphi(\varphi(32))=8 However you must first check that there is a primitive root. A PR exists if (a) n=2,4 (b) n=p^k (c)n=2p^k According to the solutions, Z_32 has no primitive roots. Is this correct? 32=2^5 which fulfills one of the conditions (b) so...
  9. M

    Complex number equation and roots of unity

    I have some math problems What is the solution to this equation : z dash(complex conjugate) = z^3 Z is complex number I try to multiply both sides by Z in the left i get Z dash Z => |Z| but i don't see the solution ---- P is primitive 9th root of unity. Calculate the sum 1 + 2P...
  10. P

    How to get roots of this complex equation

    Homework Statement hello, i am stucked at an article from sciencedirect . somewhere it gives me the following equation and then it tells that this equation must have 4 complex roots! the variable is lambda and we want to find 4 lambda complex roots Homework Equations λ^4=0The Attempt at a...
  11. M

    Finding Roots of Bivariate Polynomial Surfaces: A Slice Technique Approach

    Is there a formula for finding the roots of a bivariate polynomial in x and y with the form: (a^2)xy+abx+acy+bc Where a, b, and c are constants, of course.
  12. D

    Proving/Creating a conjecture on the roots of complex numbers

    Homework Statement Formulate a conjecture for the equation (z^3)-1=0, (z^4)-1=0 (z^5)-1=0 and prove it. Homework Equations r^n(cosnθ + isinnθ) The Attempt at a Solution Well my conjecture is that 2pi/n and 2pi/n + pi are possible values. I'm a bit iffy on how to word it. don't...
  13. D

    How Do You Manually Calculate Sixth and Eighth Roots?

    i find it puzzling how to solve this,,. (2)^1/6 or (20)^1/8 without a calculator
  14. J

    Finding roots of the derivative of a polynomial.

    hey i'm trying to figure out how to approach part b of this problem, http://imageshack.us/a/img850/6059/asdasdno.jpg so i can see that you can apply the mean value theorem to p'(x) so there exists some c between a and b such that f'(c) = [f(b) - f(a)] / (b-a)=0 so p'(x)...
  15. C

    MHB Louis's Question from YahooAnswers:Fp1 Polynomial and roots question Help?

    Question: 1.Find the range of values of \(a\) for which \[(2-3a)x^2+(4-a)x+2=0\]has real roots.2. If the roots of the equation \(4x^3+7x^2-5x-1=0\) are \(\alpha\) , \(\beta\) and \( \gamma\),find the equation whose roots are: (a) \( \alpha+1,\beta+1\) and \(\gamma+1\) (b) \(\alpha^2 \beta^2\)...
  16. S

    MHB Nth Roots of Unity Challenge Problem

    Challenge Problem $1,a_1,a_2,a_3, \cdots ,a_{n-1}$ are the $n^{\text{th}}$ roots of unity. Find the value of i) $(1-a_1)(1-a_2)(1-a_3) \cdots (1-a_{n-1})$ ii)$\displaystyle \frac{1}{2-a_1}+\frac{1}{2-a_2}+\frac{1}{2-a_3}+\cdots +\frac{1}{2-a_{n-1}}$
  17. L

    Is this an acceptable route to take for solving this integral involving roots:

    \int\frac{2}{(x+3)\sqrt{x+10}}dx _____________________________________ First thing would be u-substitution, finding what I can replace in terms of u: let u=\sqrt{x+10} \frac{du}{dx}=\frac{1}{2}(x+10)^{\frac{1}{2}-\frac{2}{2}}(x+10)' du=\frac{1}{2\sqrt{x+10}}dx → dx=2\sqrt{x+10}du...
  18. U

    Proving the Group Properties of M, the Set of Nth Roots of Unity

    Hello, Please help in solving the four set of problems, i will be very happy explaining comment as really want to understand. The problem will spread to the extent of understanding preduduschey. 1 Problems: The set M, M = {e^(j*2*pi*k/n) , k= 0,1,2...n-1} denotes the set of the nth...
  19. C

    Best ways in solving cubic equations without information on roots

    Homework Statement Learning to solve cubic equations without the knowledge of any roots, and the easiest way I found out so far is still time-consuming Homework Equations The equation and attempt is shown in the image below, tell me if its unclear :shy: The Attempt at a Solution...
  20. S

    Can You Use the Factor Theorem to Solve for Coefficients Using Known Roots?

    Homework Statement knowing a,b and c are roots 3x^3-x^2-10x+8=0 show that: 1) 1/a+1/b+1/c=5/4 2)a^2+b^2+c^2=61/9 Homework Equations factor theorem --> (x-a)(x-b)(x-c)The Attempt at a Solution can only use factor theorem: therefore (x-a)(x-b)(x-c)--> up to: x^3-x^2(a+b+c)+x(ac+bc+ab)-abc no...
  21. BloodyFrozen

    Finding Quartic Roots Without Knowing One Factor

    Is there a method to finding the roots of quartics besides Ferrari's formula? I have the equation x^{4}+5x^{2}+4x+5=0 I know one of the factor is something like $$x^{2}+x+1$$ and the other one can be found using sythetic division, but how can I find the factors without knowing one of...
  22. D

    Do Polynomial Degrees Determine the Number of Roots?

    A linear equation has 1 root A quadratic equation has 2 roots(including two equal roots and two complex roots) A cubic equation has 3 roots Is this means that the no of roots of a equation in one unknown depends on the degree of the polynomial?Why?Any proof and explanation? Thx a lot :)
  23. S

    What is the correct function f(x) to use for this limit?

    Hi guys, I'm really new to calculus and limits and have been trying to have a good crack at the following question. Sorry if I haven't written the problem out in the most acceptable format. lim (9-3√x)/(9-x) x→9 Substituting 9 gives you 0/0 and indeterminate. I tried multiplying the...
  24. N

    Square roots by approximate iterations

    Homework Statement hi every one I need to construct a C++ square root program that uses approximate values I've done the first part of the work; ********************************************************************************************************************* prompt the user for two...
  25. caffeinemachine

    MHB Irrationality of sum of roots of primes.

    I observed the following: 1) $\sqrt{2}$ is irrational. 2) $\sqrt{2}+\sqrt{3}$ is irrational(since its square is irrational). 3) $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational(assume its rational and is equal to $r$. Write $r- \sqrt{5}=\sqrt{2} + \sqrt{3}$. Now square both the sides and its...
  26. T

    The distinct roots of complex number

    I am trying to find the z0 to z6 roots of this equation but I am stuck here. Anyone care to show the step by step on how to procced?
  27. K

    How to Find Roots of Complex Numbers in Non-Linear Multi-Variable Equations?

    Homework Statement 1. z^6=(64,0) 2. z^4=(3,4) Homework Equations These are expanded out into Real and Imaginary components (treat them seperate): 1. REAL (EQ 1) - x^6-15x^4y^2+15x^2y^4-y^6=64 IMAG (EQ 2) - 6x^5y-20x^3y^3+6xy^5=0 From here, you basically solve these for all six...
  28. R

    Unique factorization domain, roots of a polynomial, abstract algebra

    Homework Statement let A be a UFD and K its field of fractions. and f\in A[x] where f(x)=x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0} is a monic polynomial. Prove that if f has a root \alpha=\frac{c}{d}\in K,K=Frac(A) then in fact \alpha\in A I need some guidance with the proof. Proof...
  29. R

    Prove roots lie inside the unit circle

    Homework Statement Let P(z)=1+2z+3z^2+...nz^(n-1). By considering (1-z)P(z) show that all the zeros of P(z) are inside the unit disk Homework Equations None given.. The Attempt at a Solution Well (1-z)P(z) = 1+z+z^2+...+nz^n and to find roots I set it to 0: 1+z+z^2+...+nz^n = 0...
  30. S

    MHB How Do You Apply the Quotient Rule with Square Roots?

    I have the answer to this problem but I am stumped as how to get there. Here it is h(x)=e^x/5/sqrt2x^2-10x+17, I'm getting stuck moving the square root up. Help
  31. T

    If the roots of a polynomial p are real, then the roots of p' are real.

    Homework Statement Let p be a polynomial. Show that the roots of p' are real if the roots of p are real. Homework Equations The Attempt at a Solution So we start with a root of p', call it r. We want to show that r is real. Judging by the condition given, I am assuming that...
  32. P

    Problem algebra involving third roots

    Homework Statement Let x = third root of [root (108) + 10] - trird root of [root (108) - 10]. Show that x ^ 3 +6 x-20 = 0 from which to infer the value of x (is a small natural) The Attempt at a Solution may can i have some ideas how to find this? i tryed to find the x but i don't know...
  33. D

    MHB Solve Repeated Roots ODE: $y' = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix}y$

    $y' = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix}y$ The characteristic equation is $$ \lambda^2 - 2\lambda + 1 = (\lambda - 1)^2 = 0. $$ So the eigenvalues are $\lambda_{1,2} = 1$. Solving $(1 - \lambda)y_1 + 2y_2 = 0\iff y_2 = -\dfrac{1}{2}(1 - \lambda)y_1$, we have $$ y = \begin{pmatrix} 1\\...
  34. C

    How can I find the roots of a polynomial like x^3-7x+6?

    Hello dear Physics Forums users. I m currently studying some Integrals from a book which my elder brother studied with years ago, and one of the problems had the denominator: x^3-7x+6 Well, I m sure that's over my level, and teacher will never ask this, but in the solution it says its...
  35. B

    How Are Square Roots Defined for Complex Numbers?

    Mod note: These posts are orginally from the thread: https://www.physicsforums.com/showthread.php?t=626545 The square root is not defined everywhere, at least not as a function, but as a multifunction, since every complex number has two square roots. I mean, the expression z1/2 is ambiguous...
  36. K

    How Do Complex Roots Transform into Trigonometric Functions in ODEs?

    Hi All I am rusty with my my math and got stumped with a straight forward question regarding vibrations and complex roots. I have a 2nd order ODE x'' +4 x' + 16 x = some forcing funciton This turns out complex roots. I go through the run around of solving this and I get a...
  37. AGNuke

    Applications of Derivative - Find no. of roots of

    if f(x) is twice differentiable function such that f(a)=0; f(b)=2; f(c)=-1; f(d)=2; f(e)=0, where a<b<c<d<e; then minimum number of zeroes of g(x) = (f'(x))2+f''(x)f(x) in the interval [a,e] is ... All I can figure out is that at the least, it is a 4-degree polynomial with roots a, (b,c) (a...
  38. M

    Taking negative/positive square roots

    Let's say that the variable 'x' is definitely some negative number. So if I wanted to solve: x^2 = 4 I get: \pm \sqrt{x^2} = \pm \sqrt{4} \pm x = \pm 2 I would have to take the positive value of 'x' and the negative value of '2' to make this true...is it okay to only take a positive square...
  39. S

    How many roots does the equation y^2 = x^3 + x + 6 (mod 5 * 9^2) have?

    What are the 4 roots of a function y^2 = x^3 + x + 6 (mod 5 * 9^2)? I don't know where to start a problem like this. The roots mod 5 are (0,1) (0,4) (2,1) (2,4) (3,1) (3,4) (4,2) (4,3) if that helps
  40. S

    Calculating Square Roots of an Elliptic Curve

    So there are four square roots for an elliptic curve represented by an equation something like this: y^2 = x^3 + x + 6 (mod 5) How would one go about calculating these?
  41. A

    Frobenius Method - Roots differ by integer

    I'm reading up on some methods to solve differential equations. My textbook states the following: "y_{1} and y_{2} are linearly independent ... since \sigma_{1}-\sigma_2 is not an integer." Where y_{1} and y_{2} are the standard Frobenius series and \sigma_1 and \sigma_2 are the roots of...
  42. C

    Solving equation with cube roots.

    Homework Statement Solve the equation: \sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0 The Attempt at a Solution What I did was move (x+3)^(1/3) to the other side, cube both sides and when I put them equal to 0 again, I managed to factor (x+2)^(1/3) out of it giving one solution x=-2...
  43. K

    Square roots in quadratic trinomial inequalities

    How do we treat expressions under a sqaure root in inequalities ? Like for ex. x+4< Math.sqrt(-x^2-8x-12) (sorry, using m.physicsforums, so i don't know what to use for a root, so JAVA :p) I request the use of this very example.
  44. T

    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    Homework Statement Find 5th roots of unity solving algebraically x^5-1=0. Using the result, find sin18 and cos18The Attempt at a Solution x^5 = 1\\ x = \sqrt[5]{1} since we have 5 roots: x_k, k = 0,1,2,3,4 \\ \\ x_k = e^{i\frac{2k\pi}{n}}, n=5 \\ x_0 = e^{i0} = 1\\ x_1 =...
  45. M

    How to find polynomial roots on a TI-83 or TI-84 Plus without PolySmlt?

    I'd like to know how to find the root of a polynomial on my TI-84 Plus without this "Polynomial Root Finder and Simultaneous Equation Solver" app. The reason is that the app's not in my calculator and I can't transfer the app to my calculator. I keep getting an "Access Denied" error message...
  46. H

    A very quick stupid question about square roots of squares

    If I see an expression like \sqrt{E^2c^2} I can just remove the square root sign right and replace it with Ec?
  47. V

    What Exactly are the Roots of a Polynomial?

    Are the roots of a polynomial given by the function f(x) defined as the values for x where f(x)=0? Does that mean f(x)=x^2 has only one root? Even though for every other value of x except zero there are two values for x that you can input to output a particular value for f(x). What about...
  48. 1

    Why Repeated Roots instead of Two Distinct Roots

    Greetings all. I hope it's OK to post here. My issue here is with the theory and not with the actual algebra or calculus. I understand this calculus question on parametric curves except why there must be a double root instead of just a repeated root in the last part. Please see the red...
  49. M

    Mathematica Find all roots of an interpolating function in Mathematica

    Hi, I've got an interpolating function which has been generated from using NDSolve and I'm trying to find all the values of x for which the y value is equal to 2. I've constructed a (much) easier example to show what I mean. Suppose I have a set of points which I have generated an...
  50. N

    Roots of unity form a cyclic group

    In a lot of places, I can read that the roots of unity form a cyclic group, however I can find no proofs. Is the reasoning as follows: Let's work in a field of characteristic zero (I think that's necessary). Let's look at the nth roots of unity, i.e. the solutions of x^n - 1. There are n...
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