1. Applying the Quadratic Formula
Adapted from Walch Education

2. 5.2.4: Applying the Quadratic Formula
A quadratic equation in standard form, ax2 + bx + c = 0, can be solved for x by using the quadratic formula:
Solutions of quadratic equations are also called roots.
The expression under the radical, b2 – 4ac, is called the discriminant.
5.2.4: Applying the Quadratic Formula

3. 5.2.4: Applying the Quadratic Formula
The Discriminant
Discriminant
Number and type
of solutions
Negative
Two complex solutions
One real, rational solution
Positive and a perfect square
Two real, rational solutions
Positive and not a perfect square
Two real, irrational solutions
5.2.4: Applying the Quadratic Formula

4. 5.2.4: Applying the Quadratic Formula
Practice #1
Use the discriminant of 3x2 – 5x + 1 = 0 to identify the number and type of solutions.
5.2.4: Applying the Quadratic Formula

5. 5.2.4: Applying the Quadratic Formula
Find the discriminant
Determine a, b, and c.
a = 3, b = –5, and c = 1
Substitute the values for a, b, and c into the formula for the discriminant, b2 – 4ac.
b2 – 4ac = (–5)2 – 4(3)(1) = 25 – 12 = 13
The discriminant of 3x2 – 5x + 1 = 0 is 13.
5.2.4: Applying the Quadratic Formula

6. Determine the number and type of solutions
The discriminant, 13, is positive, but it is not a perfect square. Therefore, there will be two real, irrational solutions.
5.2.4: Applying the Quadratic Formula

7. 5.2.4: Applying the Quadratic Formula
Solve this problem.
Solve 2x2 – 5x = 12 using the quadratic formula.
5.2.4: Applying the Quadratic Formula

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Ms. Dambreville