Question

If both the roots of $a{x}^2+bx+c=0,a\ne 0$ is positive, then

• A. $a$ and $b$ are of the same sign.
• B. $a,b$ and $c$ are of the same sign.
• C. $a$ and $c$ are of the same sign.
• D. $b$ and $c$ are of the same sign.

Answer 1

The correct option is C $a$ and $c$ are of the same sign.

As both roots are positive, so product of roots and sum of roots is positive,
$-\frac{b}{a}>0,\frac{c}{a}>0\Rightarrow \frac{b}{a}<0,\frac{c}{a}>0$
$\therefore a$ and $c$ have the same sign and opposite to $b$.