Use the Rational Root Theorem to find the roots of 12x3 8x2

Use the Rational Root Theorem to find the roots of 12x³ - 8x² - 3x + 2 = 0

12x³-8x²-3x+2=0

The constant term is 2 and the leading coefficient is 12

Factors of 2 are +-1,+-2

Factors of 12 are +-1,+-2,+-3,+-4,+-6,+-12

Rational root test yields

(+-1,+-2)/(+-1,+-2,+-3,+-4,+-6,+-12)

And on using synthetic division ,dividing by 2x-1,we get

(2x-1)(2x+1)(3x-2)=0

2x-1=0,2x+1=0,3x-2=0

x=1/2,x=-1/2,x=2/3