Question

If the zeroes of the quadratic polynomial ax² + bx + c are both negative, then a, b and c all have the ______ sign.

Answer 1

If the zeroes of the quadratic polynomial ax² + bx + c are both negative, then a, b and c all have the same sign.

Explanation:

Let the zeros be α and β, with α < 0 and β < 0. Then

α + β < 0, but `α + β = -b/a`, so `-b/a < 0` 

⇒ `b/a > 0`

⇒ a and b have the same sign.

αβ > 0, but `αβ = c/a`, so `c/a > 0`

⇒ a and c have the same sign.

Hence a, b and c all have the same sign they may be all positive or all negative.