Question

If the equation $a{x}^2+bx+c=0,a>0$ has two distinct real roots $\alpha$ and $\beta$ such that $\alpha <-5$ and $\beta >5,$ then :

• A. $c>0$
• B. $c=0$
• C. $c=\frac{a+b}{2}$
• D. $c<0$
• E. $c=a+b$

Answer 1

Answer: (D)

$c<0$

$a{x}^2+bx+c=0\alpha <-5,\beta >5$

one of the root is negative and other is positive

$\Rightarrow \alpha \beta <0\Rightarrow \frac{c}{a}<0$

Now given $a>0$

$\Rightarrow c<0$

So, option D is correct.