Roots Definition and 978 Threads

Homework Statement Barry has just solved a quadratic equation. He sees that the roots are rational, real, and unequal. This means the discriminant is a) zero, b) negative, c) a perfect square, d) a non perfect square Homework Equations The Attempt at a Solution I think the...

Hi, I am getting frustrated with trying to solve this equation: sqrt(x+9) - sqrt(x-6) = 3. I know that the answer is x=7 because of guess and check. I don't know how to show it algebraically. Squaring both sides will cancel out the x. Is there a trick or something this? Please help...

Hello guys can anyone help me solve this in MATLAB please ? http://aycu34.webshots.com/image/43953/2003131790943491216_rs.jpg

if o,p,q are roots of the equation ax^3+bx^2+cx+d=0, determine the equation whose roots are o^2,p^2 and q^2 who can help me solve it? thank you

Ok. I have a definite integral of e^sqroot(x) dx from x=0 to x=1. I would use u=sqroot(x) and du=1/2*sqroot(x), but I'm confused what I would set v=?

zero's and roots... Zero's are the same thing as roots, correct? I have a question where a) askes what's the zero's. Then b) asks what are the roots. pretty sure it's the same.

Homework Statement Hi guys, i have never taken number theory yet now I am forced to quickly understand it as it was required for a class i signed up. I need help with these problems and would greatly appreciate any hints or help in the right direction. Thanks. 1)Find with proof, all n such...

I'm having trouble understanding the idea of a weight space. Suppose \mathfrak{g} is the Lie alebra of G with maximal torus T and Cartan subalgebra \mathfrak{t}. The weights are the (1-dimensional) irreducible represenations of T. If we restrict any representation \rho : G \to GL(V) to T...

Homework Statement Find the roots of the equation z^3=-(4\sqrt{3})+4i giving your answers in the form re^{i\theta}, where r>0 and 0\leq \theta<2\pi Denoting these roots by z_1,z_2,z_3, show that, for every positive integer k. z_1^{3k}+z_2^{3k}+z_3^{3k}=3(2^{3k}e^{\frac{5}{6}k\pi i})...

Homework Statement Given Lim Cn=c, Prove that Lim\sqrt{Cn}=\sqrt{c} Homework Equations We are working from the formal definition: for all \epsilon, there exists an index N such that For all n>=N, |Cn-c|<\epsilon The Attempt at a Solution We as a group have attempted this several...

Homework Statement The roots of the equation x^3-x-1=0 are \alpha,\beta,\gamma S_n=\alpha^n +\beta^n +\gamma^n (i)Use the relation y=x^2 to show that \alpha^2,\beta^2,\gamma^2 are roots of the equation y^3-2y^2+y-1=0 (ii)Hence, or otherwise find the value of S_4 (iii)Find...

A few of the (assumed to be good) textbooks on College Algebra discuss the use of Descartes Rule of Signs, and a test for upper and lower bounds for real zeros for polynomial functions; but these ideas are never proved in the books that I found. In which college course, and in which Mathematics...

Homework Statement \frac{5}{\sqrt{7+3\sqrt{x}}} = \sqrt{7 -3\sqrt{x}} Homework Equations none The Attempt at a Solution does this equal 5 = 7 - 3\sqrt{x}

\sqrt{2+\sqrt{3}}+\sqrt{4-\sqrt{7}}=\sqrt{5+\sqrt{21}}

[SOLVED] Complex Numbers: Eigenvalues and Roots Below are some problems I am having trouble with, the computer is telling me my answers are wrong. It may be the way I am inputting the numbers but as my final is in a week and a half I would like to be sure. Thanks,

I remember learning an iterative method that gives the answer to trigonometric polynomials such as sin(x)-0.7-0.611cosx = 0 where x is the angle in degrees. The person who I learned this method from called it the method for solving transcendentals. Now I can't seem to find any...

Considering the roots of a cubic polynomial(ax^3+bx^2+cx+d),\alpha,\beta,\gamma \sum \alpha=\frac{-b}{a} \sum \alpha\beta=\frac{c}{a} \sum \alpha\beta\gamma=\frac{-d}{a} If I have those sums of roots..and I am told to find \alpha^9+\beta^9+\gamma^9[/tex] is there any easy way to find...

Homework Statement find all complex roots of z^8=81i Homework Equations The Attempt at a Solution let the angle=x z^8=r^8(cis8x) we know 81i=81 (cis pi/2) threfore z^8=81(cos pi/2 + i sin (pi/2) ) 8x= pi/2 + 2kpi x = pi/16 + kpi/4 kEz therefore...

Homework Statement Given that the roots of x^2+px+q=0 are \alpha and \beta, form an equation whose roots are \frac{1}{\alpha} and \frac{1}{\beta} b) Given that \alpha is a root of the equation x^2=2x-3 show that i)\alpha^3=\alpha-6 ii)\alpha^2-2\alpha^3=9Homework Equations...

Does anyone know how to sum a*r^(1/n) for all n?

For n a nonnegative integer, what (in terms of n) is the sum of the n-th powers of the roots of the polynomial x^6 - 1 ?

Homework Statement Show that f(x) = x^4 + 4x + c = 0 has at most 2 roots. Homework Equations The Attempt at a Solution I'm not really sure how to approach this problem, I think I have to use the IMVT / Rolle's Theorem / MVT. Any help to even get me started would be greatly...

Homework Statement Show f and g are inverse functions or state that they are not. f(x)= cube root of -8x-6 g(x)= -(x^3+6)/(8) Homework Equations You find inverses by plugging the equations into each other, if they are inverses then once you simplify the composed equation, it will equal x.The...

[SOLVED] Mean value theorem First I just want to say that my professor hasn't gotten up to teaching us this so I may be a little slow in understanding this material and want to thank you for being patient with me. The question asks to show that the equation X^4 -4X + c = 0 has at most two...

[SOLVED] Compex roots Homework Statement state the number of complex roots of each equation, then find the roots and graph the related function. x^2 + 25 = 0 Homework Equations The Attempt at a Solution x^2 + 25 = 0 so there are 2 complex roots. Once I have established that...

Homework Statement x^2\frac{d^2y}{dx^2}+ax\frac{dy}{dx}+by=0 show that if there is one real double root of the aux. eq'n show that the G.S. is given by y=c_1x^{n_1}+c_2x^{n_1}ln(x) Homework Equations Assume the trial solution y=x^n The Attempt at a Solution y=x^n...

Homework Statement Find an integer c such that the equation 4x^3 + cx - 27 = 0 has a double root. Homework Equations Ax^3+Bx^2+Cx+K = 0 Sum of Roots = -B/A Product of Roots = (-1)^n * k/a etc. The Attempt at a Solution I tried using P/Q with synthetic division to find a...

Homework Statement Write a fourth degree polynomial that has roots of 3 and 1-i. There is more than one correct solution Homework Equations The Attempt at a Solution I'm extremely lost as to where this problem is going, I know that to be a fourth degree its simply x^4, but how in...

Hello friends, I am studying in 10th class. Actually I have a question and I’m unable to solve this question. My question is: How can we find the square root of a number by hand? How about cube roots? If anybody can solve my question I will grateful. Thanks in advance!

y'' + 2y' + 5y = 0 (*) OK, what I have done is computing the two roots y1 = exp(-x)*cos2x and y2 = exp(-x)*sin2x. However, when I compute the derivatives of these two, and substitute into (*), the eq. doesn't equate 0. Are my roots wrong?

Homework Statement In the equation x^3+ax^2+bx+c=0 the coefficients a,b and c are all real. It is given that all the roots are real and greater than 1. (i) Prove that a<-3 (ii)By considering the sum of the squares of the roots,prove that a^2>2b+3 (iii)By considering the sum of the cubes of...

Homework Statement find the four fourth roots of -2\sqrt{3}+i2 i don't have any attempt for a solution because i don't know what to do.. im really lost.. i regret sleeping in class

Homework Statement Is it there a method to find out if a polynomial has no integer roots? The Attempt at a Solution I tried the division of polynomials, as well as the Horner's Method, but no luck.

Hi,.. using a Sturm or other sequence, could we find how many integer roots have the Polynomial K(x)= \sum_{n=0}^{d} a_{n}x^{n} where all the 'a_n' are integers (either positive or negative)

given a Polynomial or a trigonometric Polynomial K(z)= \sum_{n=0}^{N}a_{n}x^{n} and H(x)= \sum_{n=0}^{N}b_{n}e^{inx} is there a criterion to decide or to see if K(z) or H(x) have ONLY real roots

Does anyone know whether the graphical solution of cubic equations with real roots by means of intersecting a circle and a parabola or hyperbola (or just a parabola and hyperbola) is known or not? That solution has to give the equations for the circles, parabolas and hyperbolas involved and not...

Hi! Who knows: can any cubic root like \sqrt[3]{x} with x real be written as a form in which only square roots (real or complex) are involved?

please see my question i can't dfind its imaginary roots .the equ is X2 –3X +C,here 2 is the power of X and Cis constant we have to show that there exixts no reak number C for which the givev equation has two distinct rootss in [-1,1] i solve this by quadic formula but i got its real...

Let be a open curve on R^2 so x^{n}-c-ky=0 where k,n and c are integers, are there any methods to calculate or at least know if the curve above will have integer roots (a,b) so a^{n}-c-kb=0 ?? or perhaps to calculate the number of solutions as a sum (involving floor function) over integers of...

I don't get this problem and why the answer is what the book states that it should be: If f(x)=\sqrt{x^{2}} then f(x) can also be expressed as: l x l The answer I chose was simply x , but I don't know why it is wrong.

Homework Statement How to find the conditions on the coefficients of a quadratic equation for the roots to be outside the unit circle eg bx^2 + x - 1 = 0 where b is a constant How do we find the condition(s) that b must satisfy such that the roots of the quadratic lie outside the unit circle...

Homework Statement The following is a question from a set-text that I have chosen to explore. What digit is imediately to the right of the decimal point in (sqrt(3) + sqrt(2))^2002 Homework Equations The Attempt at a Solution I have not gone very far with this, and may need...

Hi I noticed that multiplication of all primitive roots modulo p ,p>3, congruent to 1 modulo p... I have tried some examples (13,17,19...) but i couldn't prove the general case (let g1...gk be primitive roots modulo p,p>3 ==> g1*g2*...*gk=1(p)) I need help to prove or disprove...

Excuse my typography - I'm new here... a, b, and c are rational numbers. I want to prove that * IF S = root(a) + root(b) + root(c) is rational THEN root(a), root(b) and root(c) are rational in themselves. Now I have done as follows: I reverse the problem and try to show that: * IF...

How do you do these two problems? 1. Find the sum of the 6th roots of unity. 2. Find the product of the 6th roots of unity.

Here is the question: ----------- Suppose n has a primitive root g. For which values of a (in terms of the primitive root g) does the equations x^2 \equiv a \ \text{(mod n)} have solutions? ----------- I really don't have much of an idea of how to even begin this one. Let g be a primitive...

Homework Statement We have this theorem: Let f(x)\in F[x] Then f(x) has multiple roots if and only if gcd(f(x),f'(x))=d(x) and d(x)\geq 1 We went BRIEFLY over the proof and we are supposed to be able to apply it on an upcoming exam. I'm not exactly sure how it works or what I'm...

I am trying to derive a version of Euler's criterion for the existence of cube roots modulo p, prime. So far, I have split the primes up into two cases: For p = 3k+2, every a(mod p) has a cube root. For p = 3k+1, I don't know which a it is true for, but I did a few examples and noticed...

Here is the question from the book: ------------ Determine a primitive root modulo 19, and use it to find all the primitive roots. ------------ \varphi(19)= 18 And 18 is the order of 2 modulo 19, so 2 is a primitive root modulo 19, but I am not sure of how to use that to find all...

If a is a perfect cube, a= n^3, for some integer n, and p is a prime with p is congreunt to 1 mod 3, then show that a cannot be a primitive root mod p, tat is ep(a) is not equal to p - 1