Which of the following represent the solution of the given inequality?

$x^{2} + 2 x + 5 \geq 0 \forall x \in R$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

Given: $x^{2} + 2 x + 5 \geq 0$

$\Rightarrow x^{2} + 1 + 2 x + 4 \geq 0$

Now use the identity: $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$\Rightarrow (x + 1)^{2} + 4 \geq 0$

The LHS is always positive no matter what the value of $x$ is. This is because the square of a number is always positive. And adding 4 to a positive number will also be positive. Hence ${x : x \in R}$ is the solution set. So, the entire number line is the solution.

Suggest Corrections

Similar questions

Which of the following represent the solution set of the given inequation?

$- x^{2} + 2 x + 15 > 0; x \in R$

Which of the following number line represent the solution of the inequation: $- 8 \leq 2 x < 4; x \in R$ ?

\frac{x^{2} - 1}{2 x + 5} < 3

∣ ∣ x^{2} - 2 x - 3 ∣ ∣ < ∣ ∣ x^{2} - x + 5 ∣ ∣

Which of the following graphs represent the solution of the inequation written below:

$2 x - 5 \leq 5 x + 4 < 11, x ϵ R$

Join BYJU'S Learning Program