In each case, state True if the trinomial is a perfect square else state False. $x^{2} + 14 x + 49$

True

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False

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Solution

The correct option is A True
Given that

$x^{2} + 14 x + 49$

$= x^{2} + 14 x + 7^{2}$

Split $14 x$ as:
$= x^{2} + 7 x + 7 x + 7^{2} = x (x + 7) + 7 (x + 7) = (x + 7) (x + 7)$

i.e it is a perfect square

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Similar questions

9 b^{2} + 12 b + 16

16 x^{2} - 16 x y + y^{2}

a^{2} - 10 a + 25

In each case, find whether the trinomial is a perfect square or not :

$(i) x^{2} + 14 x + 49$ $(i i) a^{2} - 10 a + 25$

$(i i i) 4 x^{2} + 4 x + 1$ $(i v) 9 b^{2} + 12 b + 16$

$(v) 16 x^{2} - 16 x y + y^{2}$ $(v i) x^{2} - 4 x + 16$

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