Question

For what values of x, the polynomial x² - 12x + 32 becomes zero ?

Hint:

The zeros of a polynomial are the solutions to the equation when the polynomial is set to zero. Factoring is often the quickest way to find these zeros.

Answer 1

We need to find the roots (or zeros) of the polynomial, which are the values of x for which the polynomial's value is 0.

We set the polynomial equal to zero and solve for x. We can use the factored form from the previous part.
x² - 12x + 32 = 0 From part (i), we know that the factored form of the polynomial is (x-4)(x-8).
So, the equation is:
(x-4)(x-8) = 0 For the product of two factors to be zero, at least one of the factors must be zero.
So, either:
x - 4 = 0 x = 4 Or:
x - 8 = 0 x = 8 The two values of x for which the polynomial becomes zero are 4 and 8.

The polynomial becomes zero for x=4 and x=8.