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Nature of Roots of Quadratic Equation.pptx

This document discusses the nature of roots of quadratic equations based on the discriminant. It defines the discriminant as the number used to describe the nature of roots, with the formula d = b^2 - 4ac. It then outlines the nature of roots for different values of the discriminant: if d > 0 the roots are two real and unequal, if d = 0 the root is one real, and if d < 0 there are no real roots. It provides examples of finding the discriminant and describing the nature of roots for quadratic equations.

Education◦
QUARTER 1 MODULE 2 LESSON 1 NATURE OF ROOTS OF QUADRATIC EQUATION
Nature of Roots of Quadratic Equation Discriminant • It is the number being used to describe the nature of roots of a quadratic equation. Formula: d = b2 – 4ac provided that the equation is in standard form. discriminant Nature of Roots d > 0 d is a perfect square Two real, rational and unequal roots d is not a perfect square Two real, irrational and unequal roots d = 0 One real and rational root. d < 0 No real root
discriminant Nature of Roots d > 0 d is a perfect square • Two real, rational and unequal roots d is not a perfect square • Two real, irrational and unequal roots d = 0 • One real and rational root. d < 0 • No real root Remember: Equation must be in standard form Example 1: Describe the nature of roots of 3t2 + 5t = 2 Solution: 3t2 + 5t = 2 3t2 + 5t – 2 = 0 a = 3, b = 5, c = –2 d = b2 – 4ac d = (5)2 – 4(3)(–2) d = 25 + 24 d = 49 Nature of Roots: Two real, rational and unequal roots
Remember: Equation must be in standard form Example 2: Compute for the discriminant of 9x2 – 12x + 4 = 0. Solution: 9x2 – 12x + 4 = 0 a = 9, b = –12, c = 4 d = b2 – 4ac d = (–12)2 – 4(9)(4) d = 144 – 144 d = 0 Nature of Roots: One real and rational root. discriminant Nature of Roots d > 0 d is a perfect square • Two real, rational and unequal roots d is not a perfect square • Two real, irrational and unequal roots d = 0 • One real and rational root. d < 0 • No real root
Remember: Equation must be in standard form Example 3: What is the nature of roots of h2 = 16 – 3h Solution: h2 = 16 – 3h h2 + 3h – 16 = 0 a = 1, b = 3, c = –16 d = b2 – 4ac d = (3)2 – 4(1)(–16) d = 9 + 64 d = 73 Nature of Roots: Two real, irrational and unequal roots discriminant Nature of Roots d > 0 d is a perfect square • Two real, rational and unequal roots d is not a perfect square • Two real, irrational and unequal roots d = 0 • One real and rational root. d < 0 • No real root
Remember: Equation must be in standard form Example 4: Describe the nature of roots of the equation 4k2 + 6k + 3 = 0 Solution: 4k2 + 6k + 3 = 0 a = 4, b = 6, c = 3 d = b2 – 4ac d = (6)2 – 4(4)(3) d = 36 – 48 d = –12 Nature of Roots: No real root discriminant Nature of Roots d > 0 d is a perfect square • Two real, rational and unequal roots d is not a perfect square • Two real, irrational and unequal roots d = 0 • One real and rational root. d < 0 • No real root
Remember: Equation must be in standard form Example 5: Determine the nature of roots of the equation 3x2 + 11x + 8 = 0 Solution: 3x2 + 11x + 8 = 0 a = 3, b = 11, c = 8 d = b2 – 4ac d = (11)2 – 4(3)(8) d = 121 – 96 d = 25 Nature of Roots: Two real, rational and unequal roots discriminant Nature of Roots d > 0 d is a perfect square • Two real, rational and unequal roots d is not a perfect square • Two real, irrational and unequal roots d = 0 • One real and rational root. d < 0 • No real root
Answer Activity 1.3: What’s More? on page 6 of your Quarter 1 Module 2
Thank you.
Nature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptx