Question

If one zero of the polynomial p(x)=x³-6x²+11x-6 is 3,find the other two zeroes.

Answer 1

Given: One zero of the polynomial p(x) = x³ - 6x² + 11x - 6 is 3.

To find: The other two zeroes.

Solution:

• Now we have given p(x) = x³ - 6x² + 11x - 6

• One root is 3, so: x - 3

• Now dividing it, we get:

               A = (x³ - 6x² + 11x - 6) / (x - 3)

• After solving this, we get:

               A = x² - 3x + 2

• Now factorising A, we get:

               x² - x - 2x + 2 = 0

               x(x - 1) -2(x - 1) = 0

               (x - 1)(x - 2) = 0

               x = 1,2

Answer:

             So the other two roots are 1 and 2 with 3.