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Question 7

There are two values of $$m$$ for which the equation $$4x^2 + mx + 8x + 9 = 0$$ has only one solution for $$x$$. The sum of these two value of $$m$$ is

Solution

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Combining the $$x$$ terms gives $$4x^2+(m+8)x+9=0$$. For exactly one solution, the discriminant is zero: $$(m+8)^2-4(4)(9)=0$$, so $$(m+8)^2=144$$ and $$m=4$$ or $$m=-20$$. Their sum is $$4+(-20)=-16$$.

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