some math help please?

Question

1. How many solutions are there to the quadratic equation
2x^2+7x+12 = 0?

a. 2
b. 1
c. 0
d. 3

2. When the discriminant equals zero, or b^2- 4ac = 0, expect ___ root(s).

3. Find the discriminant for the following quadratic equation and use it to determine the number of roots or real solutions it has.

x^2 + 3x + 15 = 0

Answer 1

1. a = 2
2. 1, it will be a double root.
b =3 a = 1 c = 15
3^2 - 4*15 = 9 - 60 = -51
A negative discriminant indicates the quadratic has two imaginary roots and no real roots.

Answer 2

1. There are no real solutions, but there are two complex (imaginary) solutions.

2. expect one root which is repeated. {a quadratic always has two roots, they may be different and real, different and imaginary, or a double root, which is the same real root twice}

3. 3^2-4(1)(15) = -51. Therefore the equation has no real roots, but has two complex roots.