Question

If the quadratic equation $a{x}^2+2bx-4=0$ ,where $a,b,c\in R$, does not have two real & distinct roots, then

• A. $a-b>1$
• B. $2b-a\le -4$
• C. $2b-a\ge -4$
• D. $a+b\le 1$

Answer 1

Answer: (C), (D)

The correct options are
C $2b-a\ge -4$
D $a+b\le 1$

Let $f\left(x\right)=a{x}^2+2bx-4$

Now, $f\left(0\right)=-4<0$.

$\therefore f\left(x\right)\le 0\forall x\in R$

Further $f(-2)=4a-4b-4\le 0\Rightarrow a-b\le 1$

$f(-1)=a-2b-4\le 0\Rightarrow 2b-a\ge -4$

$f\left(2\right)=4a+4b-4\le 0\Rightarrow a+b\le 1$