If $x^{2} + 16x + k$ is a perfect square trinomial, find $k$.

If $x^{2} + 16x + k$ is a perfect square trinomial, find $k$.
  1. $64$
  2. $32$
  3. $16$
  4. $256$

Solution

Compare with $(x+a)^{2}=x^{2}+2ax+a^{2}$. Here $2a=16\Rightarrow a=8$, so $k=a^{2}=64$.

Asked in: IMO

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