How do you solve 4x^3-12x^2-3x+9=0?

1 Answer
May 6, 2018

x=3,-sqrt3/2 or sqrt3/2

Explanation:

According to factor theorem , if f(a)=0, then (x–a) is a factor of the polynomial f(x). Converse of this theorem is also true i.e. if (x-a) is a factor of the polynomial f(x), then f(a)=0.

Here for x=3, f(x)=4x^3-12x^2-3x+9, we have

f(3)=4*3^3-12*3^2-3*3+9=108-108-9+9=0

Hence x-3 is a factor of 4x^3-12x^2-3x+9 and hence

4x^3-12x^2-3x+9=0

=>4x^2(x-3)-3(x-3)=0

or (x-3)(4x^2-3)=0

i.e. (x-3)(2x+sqrt3)(2x-sqrt3)=0

Hence x=3,-sqrt3/2 or sqrt3/2