Finding the roots and K of a quartic.[solved]
Find all roots and the value of k in the equation:
2x^4 + 3x^3 - kx^2 - 48x + 32 = 0.?
Given that the sum of 2 of the roots = 0.
I've been trying for half an hour, and I keep winding up with an equation with two variables.
I know there are 4 roots, R1, R2, R3, R4.
I said R1= R1 || R2= -R1 || R3= R3 and R4=R4.
I know S1(Sum of roots taken one at a time) = -3/2 = R3 + R4
S3 = 24 = (-R1^2 * R3) - (R1^2 * R4) - (R1R3R4)
S4 = 16 = -R1^2 * R3 * R4
What I did first was multiply the S4 eqn by 3/2, to make it = to 24. Then I set the new S4 and the S3 eqns equal to each other and worked from there. I keep getting something unsolvable.
Any help is greatly appreciated, but it'd be awesome if you could give me some steps or pointers on where I might've gone wrong.
Thanks alot in advance.
Solved. Pretty easy actually.