Applying the Quadratic Formula Adapted from Walch Education

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

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

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

5.2.4: 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

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

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

Thanks for Watching! Ms. Dambreville