# roots

1. ### Stuck with this Question based on/related to Vieta's Relations.

If p , q, r are the roots of x^3-6x^2+3x+1=0, determine the possible values of p^2q+q^2r+r^2p. Also find |(p-q)(q-r)(r-p)|. I have attached the pictures of my attempt. I need 1 more equation of the terms to find the solution. Answer :– -3, 24
2. ### Finding the roots of a 6-degree polynomial

Hello, I am having trouble finding the roots of a 6-degree polynomial equation in expression form. I hope anyone can help reduce it to a form where the expression for each root can be determine. Qx amd mx are defined values, Fx is the variable. Fx^6 and Fx^2 are the degree...
3. ### Finding the roots

Can someone please help explain step-by-step why there are no roots to this equation? : y = 2f(x - 4)

Question; If one root of ax^2 + bx + c = 0 is treble the other prove that 3b^2 - 16ac = 0 My attempt: we know that \alpha + \beta = -\frac{b}{a} \alpha \beta = \frac{c}{a} let one root be x and treble x to be 3x sum of it is 4x and the product is 3x^2 im stuck from here...
5. ### Multiplying square roots

Hey, So this: √(2t^(2)+1+2t)*√(2t^(2)+1+2t) is equal to 2t^(2)+2t+1 But I can't seem to understand how, and what rules... PLS HELP
6. ### 2-part question involving the signs applied to square roots

OK, please bear with me. This is my first post and perhaps it belongs more appropriately in some number theory forum. I'm taking an Algebra I refresher course. The first part of the question involves a statement made by the professor: "Remember that the square root of 9 is always 3 but when...
7. ### Urgent! Two exercises of roots for 2 polynoms ...

Hey, guys! I have 2 exercises, which I don't know how to solve it without Wolframalpha. 1. Find all \mathbb{R} solutions of equation: 4x^4 + 4x^3 - 11x^2 - 6x + 8 = 0. 2. Find all \mathbb{R} solutions of equation: x^4 - 4x^3 + 6x^2 - 4x - 3 = 0. I tried with formulas 4(x - A)(x - B)(x -...
8. ### Complex Roots of a Quadratic

Hi I am trying to solve a 2nd order ODE and after multiplying through by e^(theta x) the co-efficients I am left with are: a=1, b=4, c=25 I can then solve this as far as -4 plus or minus sqrt(16-100)/2 Leaving -4+- sqrt(-84)/2 I can see this can be simplified to say -4+2i(sqrt21)/2 = -2+i...
9. ### Square roots of a complex number

Suppose z^2=-8i, by letting z=x+yi. It is easy to get the two answers, 2-2i and -2+2i. We know that for real numbers \sqrt{4} refers to the positive square root of 4 i.e. 2. But what is the value of \sqrt{-8i}? which one do we choose? Is there a reason why the calculator gives 2-2i only...
10. ### Square Roots of Complex Number

find the two square roots of , giving your answers in exponential form, where r > 0 and −pi < 1 ≤ pi. I understand how to get this: But this is the answer: Where does the 3e+- pi/2 come from and how does that equal the final answer?
11. ### Finding Polynomial with 2 Roots and a Y-Intercept

Ok, my calculus teacher is a lunatic and is testing us on every concept we've ever learned in the history of math. How do I do this?? Find the g(x) using a polynomial of least degree. y-int is 16 and roots are -2 and 4 and it's not a quadratic it looks like it goes down then up then down then...
12. ### Quuadratics whose real, irrational roots are NOT conjugate pairs

Quadratics whose real, irrational roots are NOT conjugate pairs Please bear with me as I'm not sure how to articulate this question succinctly. Often, when quadratic equations have real, irrational roots, they occur in conjugate pairs, but not always. (Contrast this with imaginary roots that...
13. ### Use the given roots to factor.

5x^5-2x^4-62x^3+82x^2-67x+84 x=i,3 I know the highest degree polynomial determines how many possible roots it has. So possible is 5. also answer is: (5x-7)(x-3)(x+4)(x-i)(x+i)
14. ### Can someone help me with a few problems... having some trouble

Hi if someone could help me with the following questions that would be great! (with work) 1.Find the roots of the following equations a) 0=x^4 - 8x^2 + 16 b) 2x= 4x^3 - 2x^2 2. Find all of the zeroes in the following P(x)= x^4 - 4x^3 - 16x^2 + 21x + 18 3. Is (x+2) a factor of x^3 - 3x^2 -...
15. ### Solving roots

Is there a way to solve this? 1/(x-2) = 1/x + 1/(x-1) + 1/(x-5) + 1/(x-10) I tried combining everything and it turned into a mess. Is there another method that anyone knows? Thanks
16. ### High number of roots

So I can't remember the exact equation but how do you solve or simplify an equation that has variables xy but the beginning of the equation starts with something like (x^10)(y^8) and so on.
17. ### Primitive Roots

I have to come up with a number greater than 40 that does not have any primitive roots and explain my reasoning fully. This is for my own research and I am just familiarising myself with the topic of primitive roots as it is new to me. Is there any advice on how I should go about this that...