Question

State true or false:

If the zeros of a quadratic polynomial $a{x}^2+bx+c$ are both positive, then $a,b$ and $c$ all have the same sign.

• A. True
• B. False

Answer 1

The correct option is B False

Given quadratic polynomial is $a{x}^2+bx+c$
Let $\alpha ,\beta$ are the roots of $a{x}^2+bx+c$
$\therefore \alpha +\beta =\frac{-b}{a}$ and $\alpha \beta =\frac{c}{a}$
Given $\alpha$ and $\beta$ both are positive.
$\Rightarrow \frac{b}{a}$ is negative.

$\Rightarrow a$ and $b$ both are have different sign.
So, given statement is false.
Option B is correct.