Solve the equation 4x^3 + 32x^2 + 79x + 60 =0 given that the root is equal to the sum of the other two roots.

Question

(Hint: set roots as alpha, beta, gamma)

Answer 1

Using the factor theorem , I tried
x = ±1, ±2, ±4, and it worked if x = -4

so by synthetic division:
4x^3 + 32x^2 + 79x + 60 = (x-4)(4x^2 + 16x + 15)
= (x-4)(2x+5)(2x+3)

(x-4)(2x+5)(2x+3)=0
x = -4, or x = -5/2, or x = -3/2

and sure enough -5/2 + (-3/2)
= -8/2
= -4