Question

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

Answer 1

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`