Question

lf $x^2+2ax+b\ge c\forall x\in R$ then

• A. $b-c\ge a^2$.
• B. $c-a\ge b^2$.
• C. $a-b\ge c^2$.
• D. $a+b+c\ge 0$.

Answer 1

The correct option is A $b-c\ge a^2$.

For equation $a{x}^2+bx+c\ge 0$

Discriminant $D\le 0$

Hence for $x^2+2ax+b\ge c\Rightarrow x^2+2ax+b-c\ge 0$

$D\le 0\Rightarrow {\left(2a\right)}^2-4(b-c)\le 0$

$\Rightarrow -(b-c)\le -a^2\Rightarrow (b-c)\ge a^2$