3-Characterizing-and-Describing-the-Roots-of-Quadratic-Equations.pptx

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1. Characterizing and Describing the Roots of Quadratic Equation DOMINIC DALTON L. CALING Mathematics | Grade 9

2. Learning Objectives Characterize the roots of a quadratic equation using the discriminant. Solve for the discriminant. Identify the nature of the roots using the discriminant. Describe the relationships between the roots and the coefficients of a quadratic equation. Determine the Sum and Product of the Roots of a Quadratic Equation given the coefficients.

3. Nature of the Roots The roots of quadratic equation can be imaginary number, equal or two distinct roots. It can be determined by the value of the discriminant . Roots – also known as “solution/s”. It is the answer in solving a Quadratic equation. It the value/s of or the variable in a quadratic equation (in one variable). Discriminant – the expression inside the radical sign in the Quadratic Formula ( ). It is used to determine the Nature of the Roots .  

4. Nature of the Roots Finding the Value of the Discriminant STEPS: Write the quadratic equation in standard form. Identify the values of , , and . Substitute the values of , , and in the formula .  

5. EXAMPLES 1. 2.  

6. EXAMPLES 3. 4.  

7. Nature of the Roots Characterizing the Nature of the Roots Using the Discriminant Discriminant Nature of the Roots (the discriminant is ) Real numbers and equal (the discriminant is positive , and perfect square ) Real numbers ( rational ) and not equal (the discriminant is positive , but not perfect square ) Real numbers ( irrational) and not equal (the discriminant is negative ) No real roots (not real numbers) Discriminant Nature of the Roots Real numbers and equal Real numbers ( rational ) and not equal Real numbers ( irrational) and not equal No real roots (not real numbers)

8. Quadratic Equation Discriminant ( ) Nature of the Roots Roots Quadratic Equation Nature of the Roots Roots Real numbers and equal Real ( rational ) and not equal Real ( irrational ) and not equal No real roots                 Nature of the Roots Characterizing the Nature of the Roots Using the Discriminant

9. Sum and Product of the Roots of a Quadratic Equation Derivation of Formula

10. Sum and Product of the Roots of a Quadratic Equation STEPS: Transform the quadratic expression into standard form if necessary. Determine the values of , , and . Substitute in the formula. Check your answer by solving for the roots ( & ) of the quadratic equation then, get their sum and product. (OPTIONAL)   Sum of the Roots ( )   Product of the Roots ( )      

11. EXAMPLE 1  

12. EXAMPLE 2  

13. EXAMPLE 3  

14. Complete the table below. Quadratic Equation Roots Sum ( ) Product ( ) Quadratic Equation Roots                                                 Sum and Product of the Roots of a Quadratic Equation