Given the quadratic equation ax2 + 10x + 2 = 0, determine all values of a that will result in this equation having non-real solutions. Show all work that leads to your answer.

a>12.5.

Step-by-step explanation:

you need to look at the discriminant in the quadratic formula:

coming from the quadratic polynomial

In our case, b=10 and c=2, hence, the discriminant is

We will obtain non-real values if the discriminant is less than zero.

Therefore, this condition is written as

and we must solve for a. It yields

Hence, the answer is a>12.5.