Question

The valuesof $x^2+4x-3\forall x\in R$ lie in the interval

• A. $(-7,\infty )$
• B. $[-3,\infty )$
• C. $[-7,\infty )$
• D. $(-3,\infty )$

Answer 1

The correct option is C $[-7,\infty )$

$x^2+4x-3=x^2+4x+4-3-4$
$=(x+2{)}^2-7$

The minimum value of $(x+2{)}^2-7$ is -7, when (x+2) = 0, or when x = -2.
The maximum value of $(x+2{)}^2-7$ is $\infty$.

Thus, the value of $x^2+4x-3$ lies in the interval $[-7,\infty )$