For what value of $n$ is $x^2-10x+n$ a perfect square trinomial?

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Answer 1 · 2015-06-12T13:34:34

$n=5^2 = 25$ since every perfect square trinomial is of the form $a^2+2ab+b^2$

Every perfect square trinomial is of the form:

$a^2+2ab+b^2 = (a+b)^2$

In the given example, $a=x$ and $2ab = 2x*b = -10x$ ,

so $b=(-10x)/(2x) = -5$ and $n=b^2=(-5)^2 = 5^2 = 25$ .

For what value of nn is x^2-10x+nx^2-10x+n a perfect square trinomial?