solve this

f(x) = x^4-2x^3-7x^2+8x+12 

since, 2 and 3 are roots of this, hence one of the factors of f(x) is (x-2) (x-3) = x^2-5x+6

 

Hence, f(x) = (x^2-5x+6) (x^2+3x+2) (using long division with x^2-5x+6 as the divisor)

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

Hence, all the 4 roots are 2, 3, -2 and -1.