Let f(x) = x^2 + 4x + 1. Then - Vidyadip

MCQ

Let $f(x) = {x^2} + 4x + 1$. Then

A
$f(x) > 0$ for all $x$
B
$f(x) > 1$ when $x \ge 0$
✓
$f(x) \ge 1$ when $x \le - 4$
D
$f(x) = f( - x)$ for all $x$

✓

Answer

Correct option: C.

$f(x) \ge 1$ when $x \le - 4$

c
(c) Since $f\ (x)$ is a quadratic expression having real roots. Therefore $f\ (x)$ does not have the same sign for all $x.$

$f(x) \ge 1 \Rightarrow {x^2} + 4x + 1 \ge 1\, \Rightarrow {x^2} + 4x \ge 0$

==> $x \le - 4$or $x \ge 0$.

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