Quadratic Inequalities-mathematics 9.pptx

mathematics 9

1. Quadratic Inequalities

2. A quadratic inequality is an inequality that contains a polynomial of degree 2 and can be written in any of the following forms.

3. ax 2 + bx + c   ax 2 + bx + c   ax 2 + bx + c   ax 2 + bx + c  

4. QuQ Examples : 2x 2 + 5x + 1   s 2 9   3r 2 r   t 2 4  

5. To solve a quadratic inequality, find the roots of its corresponding equality. The points corresponding to the roots of the equality, when plotted on the number line, separates the line into two or three intervals. An interval is part of the solution of the inequality if a number in that interval makes the inequality true.

6. QuQ Examples : Find the solution set of x 2 + 7x + 12  

7. QuQ The values of a, b, and c in the equation are 2, 8, and -10, respectively. Solution

8. QuQ The Sum of the roots =   Solution The Sum of the roots =   The sum of the roots of 2x 2 + 8x -10 is -4 .

9. QuQ Product of the roots =   Solution Product of the roots =   The sum of the roots of 2x 2 + 8x -10 is -5 .

10. QuQ Example 2. Use the values of a, b, and c in finding the roots of the quadratic equation x 2 + 7x - 18 = 0

11. QuQ The values of a, b, and c in the equation are 1, 7, and -18, respectively. Solution

12. QuQ The sum of the roots =   Solution The Sum of the roots =   The sum of the roots of x 2 + 7x -18 is -7 .

13. QuQ Product of the roots =   Solution product of the roots =   The product of the roots of x 2 + 7x -18 is -18 .

14. QuQ Activity 3. This is my Sum and this is my Product. Who am I? 1.   2.   3.   4.   5.  

15. QuQ Activity 3. This is my Sum and this is my Product. Who am I? 6.   7.   8.   9.   10.