Question

Say true or false:

If the zeroes of a quadratic polynomial $a{x}^2+bx+c$ are both positive, then $a,b$ and $c$ do not have the same sign.

• A. True
• B. False

Answer 1

The correct option is A True

let the roots of equation be $e$ and $f$.

$e+f=\frac{-b}{a}$

As e and f are positive, $\frac{-b}{a}$ is also positive.

Let it be $k$.

$-b=ka$

which implies that b and a are of opposite signs

$e\times f=\frac{c}{a}$

As $ef$ is positive, $\frac{c}{a}$ is also positive

Hence, $c$ and $a$ are of the same sign and $b$ is of different sign.