Polynomials HELP (1 Viewer)

[csi]

Hi guys, I need some help with my polynomials homework. Please post up your working out if possible.

1. Find the roots of the equation x^3-15x+4=0, given that two of its roots are reciprocals. ANSWER: x= 2+root 3, 2-root 3, -4

2. Find the zeroes of the polynomial P(x)= 8x^3-14x^2+7x-1, if the zeroes form a geometric sequence (i.e. let the zeroes be α/r, α and αr. ANSWER: 1/4, 1/2,1

3. Solve 4x^3-12x^2+9x-2=0 given that two of its roots are equal. ANSWER: 1/2,1/2,2

THANKS GUYS!! Much appreciated.

 

[TheShy]

First one, let roots = alpha, 1/alpha and beta.
So if we multiply them, we get
Then if we add them the roots we should get -b/a. However as there is no x^2 term, -b/a=0. So if you add them you would get 0. You should be able to solve it from there.

Same thing with 2. If you let roots be . Multiplying them you would get alpha^3 =1/8 so alpha should be 1/2. Then you add them which should = 14/8. Find r

3. Let roots = alpha, alpha and beta. Then you multiply them to get alpha^2 beta = 1/2. Adding the roots would give 3. Then you should be able to solve simultaneously.