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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 $a$?

 May 3, 2019
 #1
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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

 

 

 

cool cool cool

 May 3, 2019

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