Roots Definition and 978 Threads

Evaluate number of real roots of the equation $$x^6-x^5+x^4-x^3+x^2-x+\frac{2}{5} = 0$$

Hello friends from afar. I ran into what I felt to be somewhat of an odd question: Prove that some odd numbers are primitive roots modulo pm for each odd prime p and each positive integer m. It feels dodgy given that any odd number n = p1p2 ⋅⋅⋅ ps cannot be a primitive root of a prime number...

Problem 1 Simplify/solve: 2*81/2-7*181/2+5*721/2-50 Attempt at solution: a1/2=√a ⇒ 2*√8 - 7*√18 + 5*√72 - 50 = 2√8 - 7√18 + 5√72 - 50 = ? Do not know how to proceed beyond this point. Have experimented with little luck. Problem 2 Simplify/solve: a-1(1+1/a2)-1/2 * (1+a2)1/2 Attempt at...

so i am starting with the equation x3 = √(3) - i first : change to a vector magnitude = √[ (√(3))2 + 12] = 2 and angle = tan-1( 1/√(3) ) = 30 degrees (in fourth quadrant) so i have a vector of 2 ∠ - 30 so i plot the vector on the graph and consider that : 1. the fundamental theorum of...

I'm currently studying the sensitivity of polynomial roots as a function of coefficient errors. Essentially, small coefficient errors of high order polynomials can lead to dramatic errors in root locations. Referring to the Wilkinson polynomial wikipedia page right...

Homework Statement Find the roots of x^4 - 6x^2 - 2 Homework EquationsThe Attempt at a Solution So my first observation is that this polynomial is irreducible by Eisenstein criterion with p=2. If I substitute y=x^2 then this polynomial becomes a quadratic, and I can apply the quadratic...

Is there a good way to relate the symmetries of the graphs of polynomials to the roots of equations? There's lots of material on the web about teaching students how to determine if the graph of a function has a symmetry of some sort, but, aside from the task of drawing the graph, I don't find...

Hello everybody after a little while :D The roots of the equation $(x+a) (x-b)= 0$ are -3 or 2. Find the value of $a$ & $b$ What should I do here ? Many Thanks :)

Hi I am writing my final Mathematics exams for Grade 12 in South Africa in 5 days. I am well prepared with an aim of getting 100%, but one concept in functions might prevent that - the concept of how the nature of roots are affected by vertical/horizontal shifts in a function, and how to...

Homework Statement Help i have a homework quiz done and i simply can't find out how to do the 3rd problem as we haven't even learned how to do it or maybe my notes aren't good or something , however I am close to an A in the class and this would help bring it closer. It asks me: "Find all the...

Homework Statement A quadratic eqn of form ax2 + bx + c = 0 is selected. The values of a, b and c are distinct and selected from 1, 2, 3, 4, 6, 8, 9. What is probability of chosen equation to have equal roots? Homework Equations root = (-b +/- Sqrt(b2-4ac)) / (2a) For equal roots b2 = 4ac[/B]...

At the beginning of the summer, I was studying a precalculus course, in which I was taught that whenever a polynomial equation has a root in the form a + sqrt(b)c or a + ib, then another root would be its conjugate, I took it for granted for that time and I thought it was intuitive. Later on...

Any suggestions on how I should approach question C1? Every time I think I have a solution I find that I have made the implicit assumption either that F is abelian or that the roots of w are in the center of F. I don't think either assumption is valid. If I let K be the root field of the poly...

Homework Statement I'm looking for an explanation to something. I've attached a picture of the solution wolfram alpha is giving me. I understand the first two zeros, +- (-1)^(1/4)*sqrt(2). But i don't understand the other two zeros with the 3/4 power. Where does that power come from...

Please take a look of the photo. In the middle part, it says For each I, by division and gets the following results. Please further explain to me how to get the result by division. The photo is attached. Attempt: 1. Using f(x)=α0(x-α1)(x-α2)...(x-αn) form. If it is divided by x-αi , there...

Using a graph of function $y=3-(x-1)^2$ which has got its negative & positive root s-0.8 and 2.7 respectively, Find an approximate value for $\sqrt{3}$. Any suggestions on how to begin? Should I be using the quadratic formula here? Many Thanks :)

Homework Statement A polynomial, P(x), is fourth degree and has all odd-integer coefficients. What is the maximum possible number of rational solutions to P(x)=0? Homework Equations P(x) = k(x-r1)(x-r2)(x-r3)(x-r4) P(x) = 0 when x = {r1, r2, r3, r4} The Attempt at a Solution I expanded the...

Hi, I drew the graph 1. Minumum value of the function = -7 can you help me to write the values for which the function is increasing interval -6<y<0 also can you help me to find the roots of the equation and obtain \sqrt{7} to the nearest decimal place. Help me to proceed Many Thanks...

Homework Statement Find the equation whose roots are given by adding 2 to the roots of the equation x^4+3x^3-13x^2-51x-36=0 Homework Equations x^4-(Σa)x³+(Σab)x²-(Σabc)x+abcd = 0 The Attempt at a Solution And the coefficient of x^3 to be -5 second coefficient = b/a = -Σa = 3 Since we are...

I'm reading "lie algebras and particle physics" by Georgi and on I'm up top where he is creating the simple algebras from simple roots and there is something I am not getting here. On page 108 he seems to be making the claim that any simple root φ had the property that any lowering operator of...

I found a strange theorem and a doubtful method in Stroud's book "Engineering mathematics": I think, every polynomial equation will have two infinite roots (at +infinity and -infinity). I also think that this method of the determination of an asymptote gives wrong results if f(x) is a...

if for rational a,b,c $ax^3+bx+c=0$ one root is product of 2 roots then that root is rational

The attachment below proves that an nth-degree polynomial has exactly ##n## roots. The outline of the proof is as follows: Suppose (1.1) has ##r## roots. Then it can be written in the form of (1.8) by factor theorem. Next use the second fundamental result in algebra (SFRA): if ##f(x)=F(x)## for...

Homework Statement Let q be a root of p(x) = x^3 + x^2 + 1 in an extention field of Z2 (integers modulus 2). Show that Z2(q) is a splitting field of p(x by finding the other roots of p(x) hint: this question can be greatly simplified by using the frobenius automorphism to find these zero's...

Hey so I'm new to my TI nspire cx, still getting the hang of it. I've been trying to figure out how to get my eigenvector values to be fractions instead of decimals when I calculate them on here. Also, when I find the polynomial roots I get back decimals instead of fractions. I would like to...

Homework Statement Question: Sum of all the solutions of the equation: ##tan^2 (33x) = cos(2x)-1## which lie in the interval ## [0, 314] ## is: (a) 5050 π (b) 4950 π (c) 5151 π (d) none of these The correct answer is: (b) 4950 π Homework Equations ## cos(2x) = 2cos^2(x) -1 ## The Attempt...

Given $a,\,b,\,c$ and $d$ are all integers such that $x=\sqrt[3]{\sqrt{8}+4}-\sqrt[3]{\sqrt{8}-4}$ is a root to the equation $ax^3+bx^2+cx+d=0$. Find the possible values for $(a,\,b,\,c,\,d)$.

Homework Statement Roots of the equation x3 - x + 1 = 0 are a, b, and c. Determine the value of a16+b16+c16 ! Homework Equations For ax3+bx2+cx+d = 0 x1+x2+x3 = -b/a x1 * x2 * x3= -d/a The Attempt at a Solution [/B] I know how to determine the value of a + b+ c but not a^16+b^16+c^16... I...

given $h+k=2016$, and the two roots $\alpha \,\, and \,\, \beta $ of equation $x^2+hx+k=0$ are all integers , please find the value of: $h,k,\alpha \,\, and \,\, \beta$

Hi everyone. I'm sorry for the long thread. If you don't want to read all the introductory stuff I will mark the part towards the end where my questions are located. I'm trying to find the general formulae for the roots of the equation $$ax^3 + bx^2 + cx + d = 0$$ By using some changes of...

Hey all, I seek to find where the derivative of a nth order polynomial is at a 0, so far I have used secant method to find it, which works, but issue is is that that returns only one root, sliding the interval could work, but then itd always point to the edge of the interval, any help...

Let the function of $f$ be a cubic polynomial such that $f(x)=x^3-\frac{3}{2}x^2+ax+b=0$, with real roots lie in the interval $(0,\,1)$. Prove that $16a+24b\le 9$. Find the corresponding function of $f$ when the equality holds.

Hello! (Wave) We consider the irreducible polynomial $g=y^4+y+1 \in \mathbb{F}_2[y]$ and let $b$ be a root of $g$. I want to find all the roots of $g$ and also three generators of $\mathbb{F}_{16}^{\ast}$ as for the basis $\{1, b, b^2, b^3 \}$. Given that $b$ is a root of $g$ we can see that...

A quadratic equation in this format x² - 2 A x + B² = 0 can be modified and expressed like: x² - 2 (u) x + (u² - v²) = 0. The roots x1 and x2 are therefore: x_1 = x_1(u,v) = u + v x_2 = x_2(u,v) = u - v Or: x_1 = x_1(a, b) = \frac{a+b}{2} + \frac{|a-b|}{2} x_2 = x_2(a, b) = \frac{a+b}{2} -...

Let $x_1,\,x_2,\,x_3$ be the three real roots of $P(x)=x^3-2x^2-x+1$ such that $x_1>x_2>x_3$. Evaluate $x_1^2x_2+x_2^2x_3+x_3^2x_1$.

Homework Statement First question = attached below Second Question = attached below Homework Equations modulus, argument, roots. The Attempt at a Solution For the 1st question I've gotten the modulus, the principal argument and the abs. of z^1/4 which was something like 1.5335 I believe. The...

Hi, I don't understand how to get to the answer of the question. The cubic equation x^3 + 3(x^2) +2 =O.by using substitution X=1/(u^0.5) get 4u^3+12u^2+9u-1 =0. I can't see where the 12 comes in It's question 10i

Let F=Z2 and let f(x) = X^3 +x+1 belong to F[x]. Suppose that a is a zero of f(x) in some extension of F. Using the field created above F(a) Show that a^2 and a^2+a are zeros of x^3+x+1?

a, b , c are positive constants and the roots of ax^2 + 2bx+ c and bx^2 + 2cx +a are all real and unequal(unique). Show that the roots of cx^2 + 2ax +b = 0 are NOT real. Help!:)

Homework Statement I've been asked to graphically verify that the system of equations F (that I've uploaded) has exactly 4 roots. And so I did, using the ContourPlot function in Mathematica and also calculated them using FindRoot. Now, I've to approximate the zeros of F using the fixed point...

Homework Statement Hi all! The problem is - 'find the condition that all roots of $$f(z)=az^3+bz^2+cz+d=0$$ have negative real part, where $$z$$ is a complex number'. The answer - $$a,b,d$$ have the same sign. Homework EquationsThe Attempt at a Solution Honestly, I have no clue about how to...

The problem is here, I'm trying to solve (b): imgur link: http://i.imgur.com/ifVm57o.jpg and the text solution is here: imgur link: http://i.imgur.com/qxPuMpu.pngI understand why there is a term in there with cte^t, it's because the A matrix has double roots for the eigenvalues. What I...

Homework Statement Calculating the roots of a quadratic with complex coefficients Homework Equations x^2 - (5i+14)x+2(5i+12)=0 The Attempt at a Solution I tried the quadratic solution but it gives too complicated solutions. I have no idea on how to do this...

Can someone explain to me what are real roots?

Homework Statement I am supposed to find the roots of the equation: 10esinx = x2 - 5x +4 in MATLAB using Newton's method with a tolerance of 10-8. There should be three roots. Homework Equations p=po - f(po)/f'(po) |p - po| < TOL The Attempt at a Solution Here is what I have for the code...

1)y^3+6y^2+11y+6=0 2)y^3+6y^2+12y+8=0 find it's root and tell me how you obtained it.

Given two points in x-axis, a and b, is possible formulate a quadratic equation whose roots intersects a and b: (x-a)(x-b)=0 So, is possible make the same with a conic equation? Given 4 points, two in x-axis (a and b) and two in y-axis (c and d), is possible reconstitute a conic equation whose...

So I stumbled upon this problem: Solve: And I have attempted to solve it, however my solution doesn't match that of the book. The solution should be x+4, but I don't have a clue how to get to that. I'm sorry if this seems pretty rudimentary, but I just want some help because it's the first...

[Thread moved to homework forum by a Mentor] the exercise was to find the roots of x^8 - 5x^6 + 7x^4 - 5x^2 +6=0 I substituded x^2 with y : y^4 - 5y^3 + 7y^2 - 5y +6=0 I factored this by doing the rational roots test and trying those possible roots with the method of horner and got (y-2)...

Let $a, b, c, d, e$, and $f$ be the roots of $x^6 + 15x^5 + 53x^4 -127x^3 -1038x^2 -1832x- 960 = 0.$ Find $\displaystyle \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}+\frac{1}{e}+\frac{1}{f}.$