There are two values of a for which the equation 5x^2 + ax + 7x + 5 = 0 has only one solution for x. What...

Question

There are two values of a for which the equation 5x^2 + ax + 7x + 5 = 0 has only one solution for x. What is the sum of those values of a?

SnapAndSolve AI · Accepted Answer

For the quadratic equation 5x^2 + (a+7)x + 5 = 0 to have only one solution, the discriminant must be zero. The discriminant Δ is given by:

Δ = b^2 - 4ac

Here, a = 5, b = a+7, and c = 5. So:

Δ = (a+7)^2 - 4(5)(5)

Setting Δ to zero for one solution:

(a+7)^2 - 100 = 0

(a+7)^2 = 100

Taking the square root of both sides:

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

Solving for a:

The sum of these values is:

3 + (-17) = -14

Answer