1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f(x) be a quadratic expression which is positive for all real values of x, then for all real x, 10 (f(x) + f(-x)) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $f(x)$ be a quadratic expression which is positive for all real values of $x$, then for all real $x, 10 (f(x) + f(-x)) $ is

Complex Numbers and Quadratic Equations

Solution:

Let. $f(x) = ax^2 + bx + c$
Since $f(x)$ is +ve for all real values of $x$
$\therefore \, a, b, c > 0$. $f(- x) = ax^2 - bx + c $
$\therefore \, f(x) + f(- x) = 2 (ax^2 + c) > 0$
$\therefore \, 10[f(x) + f(-x)] > 0 $