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

##### 1 Answer

Mar 26, 2017

#### 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#