Solving the roots of Quadratic Equation.pptx

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1. The Nature of the Roots of a Quadratic Equation

2. The value of the expression is called the discriminant of the quadratic equation ax 2  + bx + c = 0.   2

3. If is zero then the roots are real numbers and equal.   If is greater than zero and a perfect square then the roots are rational numbers and not equal.   If is greater than zero and not a perfect square then the roots are irrational numbers and not equal.   If is less than zero then the equation has no real roots.  

4. Describe the roots of the quadratic equation: Since is zero then the roots are real numbers and equal.   a = 1   b = -4 c = 4        

5. Describe the roots of the quadratic equation: Since is greater than zero and a perfect square then the roots are rational numbers and not equal.   a = 1   b = 7 c = 10        

6. Describe the roots of the quadratic equation: Since is greater than zero and not a perfect square then the roots are irrational numbers and not equal.   a = 1   b = 6 c = 3        

7. Describe the roots of the quadratic equation: Since is less than zero then the equation has no real roots.   a = 1   b = 2 c = 5        

8. Describe the roots of the quadratic equation:     Nature of roots       Nature of roots       Nature of roots     real numbers and equal.   rational numbers and not equal.   rational numbers and not equal.     Nature of roots     no real roots.

9. The Sum and Product of Roots of Quadratic Equations

10. The sum of roots of quadratic equation   10 The product of roots of quadratic equation  

11. Case 1: Find the sum and product of roots of the quadratic equation. 1.   a = 2 b = 8 c = -10                                  

12. Shortcut in finding the sum and product of roots             1.   a = 2 b = 8 c = -10   -5 FACTORS SUM -1 5 4 1 -5 -4      

13. Find the sum and product of roots             2 .   a = 1 b = 7 c = -18   -18 FACTORS SUM 1 -18 -17 -1 18 17 2 -9 -7 -2 9 7 3 -6 -3 -3 6 3      

14. Find the sum and product of roots             3 .   a = 1 b = 4 c = 3   3 FACTORS SUM 1 3 4 -1 -3 -4      

15. Find the sum and product of roots             4 .   a = 6 b = 12 c = -18   -3 FACTORS SUM 1 -3 -2 -1 3 2      

16. Find the quadratic equation in standard form   5 .                  

17. Find the quadratic equation in standard form   6 .                  

18. Find the quadratic equation in standard form   7 .                  

19. Equations Transformable into Quadratic Equations

20. Solving Quadratic Equations That Are Not Written in Standard Form 1 .              

21. Solving Quadratic Equations That Are Not Written in Standard Form 2 .              

22. Solving Rational Algebraic Equations Transformable into Quadratic Equations 1 .