MATHEMATICS 9 5TH MODULE NAME: Meloupe Grace M. Alburo THE DISCRIMINANT Exploring Math You have derived the quadratic formula in the proceeding lesson. Can you now solve each equation in the table? Record the value of b- 4ac and the value or values of the roots. Can you describe the nature of the solutions as shown below. Equation b-4ac Roots Description two real and unequal 3x² + 4x+1=0 4 x=13 x-1 roots ✓ 2x² + 9x + 11 = 0 2x² - 6x +9=0 -2x² + 8x + 24 = 0 -2x² + 6x-10=0 + 4x + 9-0 5x² + 2x-10-0 When the solutions to a quadratic equation are not real numbers, do they show any special relationship to each other? Describe any pattern that you find in your table. How can you use the value of b²-4ac to describe the nature of the roots of a quadratic equation? You can determine the nature of the roots without actually solving the equation. Let x, and x, denote the roots of ar²+bx+c = 0, where a, b and c are real numbers, and a # 0. Using the quadratic formula, you come up with X₁ -b+√b²-4ac 2a and X₂ -b-√b²-4ac 2a The number represented by b² - 4ac, under the radical sign is called the discriminant of the quadratic equation. The nature of the roots can be determined by finding the value of the discriminant. Consider the following examples:

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