Question

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

• A. $b^2-4ac>0$
• B. $c<0$
• C. $a+|b|+c>0$
• D. $4a+2|b|+c<0$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $c<0$
B $b^2-4ac>0$
D $4a+2|b|+c<0$

$f\left(x\right)={ax}^2+bx+c=0,\alpha <-2,\beta >2,a>0\therefore f\left(0\right)<0f\left(0\right)=0+0+c<0\therefore c<0D>0\therefore b^2-4ac>0f\left(2\right)<04a+2b+c<0\therefore 4a+2|b|+c<0f(-2)<0\therefore 4a-2b+c<0$