For what value of n is x^2-11x+n a perfect square trinomial?

1 Answer
Jul 1, 2015

Answer:

If #n=121/4# the #x^2-11x+n# is a perfect square trinomial.

Explanation:

For a perfect square:
#color(white)("XXXX")##(x-a)^2 = color(red)(x^2-2ax)+color(blue)(a^2)#

If #color(red)(x^2-11x)# are the first two terms of such a perfect square
then #color(red)(2ax) = color(red)(11x)#
#rarr color(red)(a) = 11/2#
and (since we want #n# to be the third term)
#color(white)("XXXX")##color(blue)(n)=color(blue)(a^2) = 121/4#