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Nature of Roots

If the roots ...

Question

If the roots of the quadratic equation $x^{2} + (p + 2) x + (2 p + 5) = 0$ is real. Which of the following is true?

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Solution

The correct option is A

Compare $x^{2} + (p + 2) x + (2 p + 5) = 0 b y a x^{2} + b x + c = 0$

a = 1, b = p + 2 and c = 2p + 5

So, if roots are real Discriminant D $\geq$ 0

$b^{2} - 4 a c \geq 0$ ${(p + 2)}^{2} - 4 (2 p + 5) \geq 0$

$p^{2} + 4 + 4 p - 8 p - 20 \geq 0$ $p^{2} - 4 p - 16 \geq 0$

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