Question

There are two values of a for which the equation 5x2+ax+7x+5=0 has only one solution for x. What is the sum of those values of a?

Answer 1

Answer:

-14

Step-by-step explanation:

First of all, we know that 5x^2+ ax+7x +5=0 only has one root. That means that b^2 - 4ac=0, and we can use this to find the discriminant, ax + 7x.

Now, if we simplified 5x^2+ ax+7x +5=0, by dividing it all by 5, it would be x^2+(a+7)/5x + 1 = 0.

After, we can plug what we know into the formula, b^2 - 4ac=0. It would be:

(a+7)^2 / 25 - 4 = 0

(a+7)^2 / 25 = 4

(a+7)^2 = 100

Since this is a square root, a+7 can be both negative or positive.

a+7= 10, or a+7 = -10

a=3, or a=-17

The question asks for the sum of a, which is 3 + (-17) = -14

Therefore, the answer is -14.

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