Find the discriminant of the quadratic equation x2 + 6x + 14 = 0 and use it to determine the number and types of solutions.
b2 − 4ac
a.)−20; two nonreal solutions
b.)−20; one real solution
c.)92; two real solutions
d.)92; one real solution

The correct option is A) −20; Two non-real solutions

Step-by-step explanation:

Consider the provided equation.

Now compare the provided equation with the standard form of quadratic equation:

The discriminant of the quadratic equation can be calculated as:

If , then the equation has two non-real solutions.

If , then the equation has one real solutions.

If , then the equation has two real solutions.

Now by the comparison of the provided equation with the standard from, it can be concluded that a = 1, b = 6 and c = 14.

Substitute the respective values in the discriminant formula:

The value of D is -20 which is less than 0 thus the equation has two non real solutions.

Hence, the correct option is A) −20; Two non-real solutions