Question

Given that the equation 12x^3-4x^2-5x+2 has 2 equal zeros find all zeros

Answer 1

f(x)=2xcube-4x square-5x+2

f'(x)=36x square-8x-5

1/2 satisfy f'(x) so two roots are 1/2 so product of roots is equal to-1/6

therefore 1/4 ×alpha=--1/6

therefore alpha=-2/3

Answer 2

please see the attachment