4-Roots-and-Coefficients-of-Quadratic-Equations.pptx

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1. Roots And Coefficients Of Quadratic Equations DOMINIC DALTON L. CALING Mathematics | Grade 9

2. Discriminant The radicand ( ) in the quadratic formula  

3. Using the Discriminant Given a quadratic equation in the form of , where a, b, and c are real numbers and . We can determine the number and type of solutions of a quadratic equation, by evaluating the discriminant.  

4. Using the Discriminant If > 0, the equation has two real solutions. Both will be rational if the discriminant is a perfect square or irrational, otherwise.  

5. Using the Discriminant If = 0, the equation has only one solution which will be a rational number.  

6. Using the Discriminant If < 0, the equation has no real number solution.  

7. EXAMPLE  

8. Relation of Roots The sum of the roots is the additive inverse of the quotient of b and a  

9. Relation of Roots The product of the roots is the quotient of c and a  

10. Relation of Roots The relations that exist between the roots of a quadratic equation which can be used in checking the validity of the roots can be of best use in deriving the quadratic equation.

11. General Form: Expressed in the form of Multiplication Property of Equality:  

12. Rule To derive the quadratic equation when the two roots are given, subtract each root from x to get the corresponding linear factors and equate the product of the linear factors to zero.

13. EXAMPLE  

14. EXAMPLE Find a quadratic equation whose roots are -1 and 2.

15. EXAMPLE Find a quadratic equation whose roots are 5 and -6.

16. EXAMPLE Find a quadratic equation whose roots are 0 and 3.

17. EXAMPLE Find a quadratic equation whose roots are -2 and .