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Nature of Roots

If equation ...

Question

If equation $x^{2} + 8 x + p = 0$ has real and distinct roots then

p \geq 16

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p > 16

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p < 16

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p \leq 16

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Solution

The correct option is C $p < 16$
$Δ > 0$ for real and distinct roots
$b^{2} - 4 a c > 0$
$a = 1, b = 8, c = p$
${(8)}^{2} - 4 (1) (p) > 0$
$64 - 4 p > 0$
$64 > 4 p$
$p < 16$

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