# roots

1. ### B Properties of roots of polynomials

i have some doubts from chapter 1 of the book Mathematical methods for physics and engineering. i have attached 2 screenshots to exactly point my doubts. in the first screenshot...could you tell me why exactly the 3 values of f(x) are equal. the first is the very definition of polynomials...but...
2. ### B Questions regarding polynomial divisions and their roots

Hello everyone, Going through calculus study, there is a vague point regarding polynomials I'd like to make clear. Say there's a polynomial $f$ with a root at $a$ with multiplicity $2$, i.e. $f(x)=(x-a)^2g(x)$ where $g$ is some other polynomial. I define $h(x)=\frac {f(x)} {x-a}$...
3. D

### I Need help solving for X in third order polynomial

Hello I have a third order polynomial, for example y(x) = -60000x^3 - 260x^2 + 780x + 0.6 I need to know what is x at y = 28 and/or y= 32. I can goto matlab and find the roots ( x = - .1158, -.0007, and .1122 ) or I can go to http://www.wolframalpha.com and it also finds the roots and...
4. ### I Can Taylor series be used to get the roots of a polynomial?

I'm using this method: First, write the polynomial in this form: $$a_nx^n+a_{n-1}x^{n-1}+......a_2x^2+a_1x=c$$ Let the LHS of this expression be the function $f(x)$. I'm gonna write the Taylor series of $f^{-1}(x)$ around $x=0$ and then put $x=c$ in it to get $f^{-1}(c)$ which will be...
5. ### Prove: polynomial is uniquely defined by three of its values

Homework Statement Algebra - I.M. Gelfand, Problem 164. Prove that a polynomial of degree not exceeding 2 is defined uniquely by three of its values. This means that if P(x) and Q(x) are polynomials of degree not exceeding 2 and P(x1) = Q(x1), P(x2) = Q(x2), P(x3) = Q(x3) for three different...
6. ### A How is this 'root stability' differential equation derived?

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...
7. ### B Help with understanding Nature of Roots for Quadratic and Cu

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...
8. ### Can't find all the zeroes of a polynomial

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 im close to an A in the class and this would help bring it closer. It asks me: "Find all the...
9. ### Finding sum of roots of trigonometric equation

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...
10. ### Sum of roots^16

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...
11. ### Factoring equation with real coefficients

Homework Statement Find the roots of z^4+4=0 and use that to factor the expression into quadratic factors with real coefficients. Homework Equations DeMoivre's formula. The Attempt at a Solution I have been able to identify they are \pm 1 \pm i but i have no idea how to factor the...
12. ### Integral with roots on bottom and top

It's the integral of sqrt(x)/(cubed root(x) + 1) I tried regular u substitution but that didn't let me get rid of all the x's. I also just tried long division but that gave me an answer that didn't match with the actual answer to the problem. The actual answer is 6[1/7 x^(7/6) - 1/5 x^(5/6) +...