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For what value of $k$ is $x^2-21x+k$ a perfect square trinomial?

1 Answer

Mar 26, 2017

$k = 441/4 = 110.25$

Explanation:

Suppose:

$x^2-21x+k = (x+e)^2$

$color(white)(x^2-21x+k) = x^2+2ex+e^2$

Equating coefficients, we have:

$2e=-21$

So:

$e = -21/2$

and

$k = e^2 = (-21/2)^2 = 441/4 = 110.25$

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