Question

If a + b + c = 0, then a zero of the polynomial ax² + bx + c, is _________.

Answer 1

Let f(x) = ax² + bx + c

It is given that 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 + b + c = 0, then a zero of the polynomial ax² + bx + c, is 1.