Question

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

• A. $a<0,c<0$
• B. $a<0,c>0$
• C. $a>0,c<0$
• D. $a>0,c>0$

Answer 1

The correct option is A $a<0,c<0$

Let $r$ and $s$ be the roots of equation then we know $r+s=\frac{-b}{a}$ and as L.H.S. is negative R.H.S. will also be negative.

As $b<0,a$ has to be negative.

Now $r\ast s=\frac{c}{a}$ and as L.H.S. is positive R.H.S. also has to be positive.

Thus $a$ and $c$ are of same sign and are negative.

Hence $a<0,c<0$