Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
combine like terms and
arrange as ax2 + bx + c x2 + (k – 9) • x + 16
For the quadratic to be the square of a binomial, the "b" term
has to be twice the value of the square root of the "c" term.
k – 9 = (2)(+4) ==>> k = ( +8 + 9 )
when k = 17 ==>> x2 + (17 – 9) • x + 16 = (x + 4)2
when k = 1 ==>> x2 + ( 1 – 9) • x + 16 = (x – 4)2
sum of both values of k = 18
.