USE THE DESCRIMINANT TO FIND THE NUMBER OF REAL SOLUTIONS OF 2 X (SQUARED) +9X +7=0

Question

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

Answer 1

The discriminant is the expression under the radical in the quadratic formula: b² - 4ac, where the quadratic is of the form ax² + bx + c. In this case, a = 2, b = 9, and c = 7.

b² - 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.