Question

Determine the number and type of solutions for the equation x^2+8x+15=0

Two different irrational-number solutions
One repeated irrational-number solution
One repeated rational-number solution
Two different rational-number solutions
Two imaginary-number solutions

Answer 1

Explanation:

disc=8²-4×1×15=64-60=4=2²>0

it is a perfect square and >0

so it has one repeated rational number solution.

Answer 2

I think there are two different rational-number solutions because if you try to solve it through factoring, you can see that it factors to (x+3) and (x+5), which means the solutions would be x = -3, -5.
And those are two different rational numbers.