Q. If $x^{2} + 2ax + b \geq c,\ \forall x \in R$, then
A) $a - c \geq a^{2}$
B) $c - a \geq b^{2}$
C) $a - b \geq c^{2}$
D) None of these
Explanation
(a)
Let, $f(x) = x^{2} + 2ax + b$
$= (x + a)^{2} + b - a^{2}$
So, minimum value of $f(x) = b - a^{2}$.
Since, $f(x) \geq c,\ \forall x \in R\ hence\ b - a^{2} \geq c$
$ie,\ b - c \geq a^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.