Evaluate the discriminant for the following equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. 5 x squared plus 11 x plus 6 equals 0

The Solutions are distinct and rational

Step-by-step explanation:

Given the general form of a quadratic equation: ax²+bx+c=0

The discriminant D=b²-4ac is used to determine the nature of the roots of the quadratic equation.

There are three cases:

1. If b² - 4ac > 0

The quadratic equation has two real, distinct (different) roots.

2. If b² - 4ac < 0

The quadratic equation has no real roots. i. e. It has complex roots

3. If b² - 4ac = 0

The quadratic equation has two real, identical roots.

Given our equation:

5x²+11x+6=0

a=5, b=11, c=6

The discriminant:

D=b²-4ac=11²-4 (5) (6) = 1

Since D=1>0, the roots of the equation are real and distinct.