2021/021)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 these values of a?  (A) -16 (B) -8 (C) 0 (D) 8  

say 8+ a =m

$4x^2+ mx + 9$ has only one solution for x only if $4x^2+ mx + 9$ is a perfect square

or $4x^2+ mx + 9= (2x\pm 3)^3$

Taking $(2x+3)^2$ we get m = 12 or 8+a = 12 or a = 4

Taking $(2x-3)^2$ we get m = -12 or 8+a = -12 or a = -20

so sum of a = -16 so ans (D)