Question

Find all the roots of (x^3) - (6x^2) + 11x -6.
Please be fast!!!

Answer 1

Let p(x) = x³ - 6x² + 11x - 6 =0
           ⇒ x³ - x² - 5x² + 5x + 6x - 6 =0
           ⇒ x²(x-1) - 5x(x-1) + 6(x-1) =0
           ⇒ (x-1) (x² - 5x + 6) =0
           ⇒ (x-1) (x² - 2x - 3x + 6) =0
           ⇒ (x-1) {x(x-2) - 3(x-2)} =0
           ⇒ (x-1) (x-2) (x-3) =0
.·.Roots of the equation are 1,2 and 3