if the zeroes of a quadratic polynomial ax2 +bx +c are both negative then a, b, c all have the - Maths - Quadratic Equations

Question

if the zeroes of a quadratic polynomial ax2 +bx +c are both
negative then a, b, c all have the same sign state true or false
and justify your answer

Lalit Mehra · Accepted Answer

The given quadratic polynomial is ax2 + bx + c Let âˆ and Î² be the zero of the given quadratic polynomial $∴ α + β = \frac{- b}{a} and α β = \frac{c}{a}$ Given, âˆ and Î² are both negative âˆ´ âˆ + Î² is negative and âˆ Î² is positive $\Rightarrow \frac{b}{a}$ is positive and $\frac{c}{a}$ is positive â‡’ a, b, c are all positive or a, b, c are all negative Hence, a, b and c all have same sign

if the zeroes of a quadratic polynomial ax2 +bx +c are both negative then a, b, c all have the same sign. state true or false and justify your answer