Nature of Roots of Quadratic Equation.pptx

This powerpoint presentation is one of the lesson on Grade 9 about nature of the roots of quadratic equation. It is described here the nature of its roots and how to compute it roots. I hope this material will help others

1. QUARTER 1 MODULE 2 LESSON 1 NATURE OF ROOTS OF QUADRATIC EQUATION

2. 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 = b 2 – 4 ac 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

3. 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 3t 2 + 5t = 2 Solution: 3t 2 + 5t = 2 3 t 2 + 5 t – 2 = 0 a = 3 , b = 5 , c = –2   d = b 2 – 4 a c d = ( 5 ) 2 – 4( 3 )( –2 ) d = 25 + 24 d = 49 Nature of Roots : Two real, rational and unequal roots

4. Remember: Equation must be in standard form Example 2 : Compute for the discriminant of 9x 2 – 12x + 4 = 0. Solution: 9 x 2 – 12 x + 4 = 0 a = 9 , b = –12 , c = 4   d = b 2 – 4 a c 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

5. Remember: Equation must be in standard form Example 3 : What is the nature of roots of h 2 = 16 – 3h   Solution: h 2 = 16 – 3h h 2 + 3 h – 16 = 0 a = 1 , b = 3 , c = –16   d = b 2 – 4 a c 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

6. Remember: Equation must be in standard form Example 4 : Describe the nature of roots of the equation 4k 2 + 6k + 3 = 0   Solution: 4 k 2 + 6 k + 3 = 0 a = 4 , b = 6 , c = 3   d = b 2 – 4 a c 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

7. Remember: Equation must be in standard form Example 5 : Determine the nature of roots of the equation 3x 2 + 11x + 8 = 0 Solution: 3 x 2 + 11 x + 8 = 0 a = 3 , b = 11 , c = 8   d = b 2 – 4 a c 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

8. Answer Activity 1.3: What’s More? on page 6 of your Quarter 1 Module 2

9. Thank you.