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

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 (A) > 0 (B) ≥ 0 (C) < 0 (D) ≤ 0

Tardigrade Admin · Accepted Answer

Let. f(x) = ax2 + bx + c Since f(x) is +ve for all real values of x ∴ a, b, c > 0. f(- x) = ax2 - bx + c ∴ f(x) + f(- x) = 2 (ax2 + c) > 0 ∴ 10[f(x) + f(-x)] > 0

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

$> 0$

$\geq 0$

$< 0$

$\leq 0$

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

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

>0

≥0

<0

≤0