Question

Consider the polynomial equation x(x - 3)(x + 6) (x-7) -0. Which of the following are zoros of the

equation? Select all that apply.

Answer 1

The zeros are : 0, 3, -6, 7.

Explanation:

Zeros of a polynomial is the values at which the polynomial becomes zero. They are also called the roots of the polynomial.

When (x - a)(x - b) = 0, we can say that either (x - a) = 0 or (x - b) = 0. At least one zero renders the whole equation to be zero.

Now, we are given that: x. (x - 3). (x + 6). (x - 7) = 0

⇒ To make the equation zero, at least one of the following should be true:

x = 0

x - 3 = 0 ⇒ x = 3

x + 6 = 0 ⇒ x = -6

x - 7 = 0 ⇒ x = 7

Therefore, x can take any one of the above values and that would make the polynomial zero.