Question

If a + c = b, then a zero of the polynomial ax² + bx + c, is _________.

Answer 1

Let f(x) = ax² + bx + c

It is given that a + c = b
⇒ a − b + c = 0

Therefore, when x = −1, f(x) = $a{\left(-1\right)}^2+b\left(-1\right)+c=a-b+c=0$

Thus, x = −1 is the zero of f(x).

Hence, if a + c = b, then a zero of the polynomial ax² + bx + c, is −1.