Question

If both the roots of $a{x}^2+bx+c=0$ are negative and $b<0$, then which of the following statements is always true?

• 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 D $a<0,c<0$

When the roots are negative, then the $x$ coordinate of vertex of the parabola is also negative.
$-\frac{b}{2a}<0\Rightarrow a<0(\because b<0)$
The graph of the parabola will be like,


The graph will intersect with negative $y-$axis, so
$c<0$

Hence, $a<0,c<0$