Question

If both the roots of $a{x}^2+bx+c=0$ are real and negative, then

• A. $ab>0,bc<0$
• B. $ab>0,ac>0$
• C. $ab>0,ac<0$
• D. $ab<0,bc<0$

Answer 1

The correct option is B $ab>0,ac>0$

Given equation is $a{x}^2+bx+c=0$

Let the roots are $\alpha$ and $\beta$

Both the roots are negative.

So,sum of roots is negative
$\Rightarrow \alpha +\beta <0$
$\Rightarrow -\frac{b}{a}<0$
$\Rightarrow -ab<0$ (mulitplying by $a^2$,$a^2$ is always positive, the sign will remain the same)

$\Rightarrow ab>0$

Also, product of roots should be positive

$\alpha \beta >0$
$\Rightarrow \frac{c}{a}>0$
$\Rightarrow ac>0$ (Multiplying by $a^2$)

So, Op $B$ is correct