Use the quadratic equation x2+3x+5=0 to answer the questions.

A: What is the discriminant of the quadratic equation?

B: Based on the discriminant, which statement about the number and type of solutions to the equation is correct?

Select one answer choice for part A, and select one answer choice for part B.

A: 11
A: 29
A: −11
A: −29
B: The equation has two complex solutions.
B: The equation has one repeated real solution.
B: The equation has two real solutions.

The discriminant is found within the quadratic formula. It tells us what type of solutions we will expect to have when we solve it. If we get a positive number, we expect to have 2 real solutions to our quadratic; if we get a 0, we expect to have 1 real solution that is "used" twice; if we get a negative number, we expect to have 2 complex solutions to our quadratic. In our quadratic,

a = 1, b = 3, c = 5. So filling in the determinant formula, b² - 4(a)(c):

3² - 4(1)(5)

which gives us -11 (part A of your answer).

Since it is negative, part B is

The equation has two complex solutions