USE DISCRIMININT TO FIND THE NUMBER OF REAL SOLUTIONS OF 2X(SQUARED) +9X+7

The discriminant is the expression under the radical in the quadratic formula: **b ^{2}
**

**-**

**4ac**, where the quadratic is of the form ax

^{2}+ bx + c. In this case, a = 2, b = 9, and c = 7.

b^{2} - 4ac = (9)^{2} - 4(2)(7) = 81 - 56 = 25

These are the rules for determining the nature of the roots of a quadratic based on the discriminant:

(1) If the discriminant = 0, then there is one real solution

(2) If the discriminant > 0, then there are two real solutions

(3) If the discriminant < 0, then there are two imaginary solutions

In this example, the discriminant = 25, which is greater than 0. Therefore, there are two real solutions to this quadratic equation.