State the whether given statement is true or false
Prove that $x^{2} + 6 x + 15$ has no zero.

True

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False

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Solution

The correct option is A True
$x^{2} + 6 x + 15$
$= {(x + 3)}^{2} + 15 - 9$
$= {(x + 3)}^{2} + 6$
Now ${(x + 3)}^{2} \geq 0$
$∴ {(x + 3)}^{2} + 6 \geq 6$
$∴$ since it is greater than or equal top $6$ , it can never be equal to $0$
Hence Proved

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