There are two values of $a$ for which the equation $4x^2+ax+8x+9=0$ has only one solution for $x$. What is the sum of those values of $a$?

Guest May 3, 2019

#1**+1 **

4x^2 + ax + 8x + 9 = 0

4x^2 + (8 + a)x + 9 = 0

If one solution, the discriminant = 0....so....

(8 + a)^2 - 4(4)(9) = 0

64 + 16a + a^2 - 144 = 0 simplify

a^2 + 16a - 80 = 0 factor

(a + 20) ( a - 4) = 0

Setting both factors to 0 and solving for a gives that a = -20 or a = 4

And the sum of these = -16

CPhill May 3, 2019