Lesson 6 - Discriminant of Quadratic Equation.pptx

yes

1. MATH 9 WELCOME TO OUR ONLINE CLASS!

2. Discriminant of Quadratic Equation

3. What is Discriminant? I n the quadratic formula x = , the expresssion b² - 4ac is the discriminant of quadratic equation.  

4. Value of the discriminant Nature of the solution/roots Positive & perfect square Two Different Rational Numbers Positive but not a perfect square Two Different Irrational Numbers Zero Two Equal Rational Numbers Negative Two Different Imaginary Numbers

5. Example # 1 2x² - 6x - 8 = 0 a = 2 b = -6 c = -8 b² - 4ac (-6) ² - 4(2)(-8) 36 + 64 100 Positive and a Perfect Square To check, solve for the roots. X = X = X =   X = X = 16/4 x = -4/4 X = 4 x = -1   Two Different Rational Numbers

6. Example # 2 x² + x = 5 a = 1 b = 1 c = -5 b² - 4ac (1) ² - 4(1)(-5) 1 + 20 21 Positive but not a Perfect Square To check, solve for the roots. X = X = X =   X =   Two Different Irrational Numbers (x² + x - 5 = 0)

7. Example # 3 x² + 4x + 4 = 0 a = 1 b = 4 c = 4 b² - 4ac (4) ² - 4(1)(4) 16 – 16 Zero To check, solve for the roots. X = X = X =   X = X = -4/2 x = -4/2 X = -2 x = -2   Two Equal Rational Numbers

8. Example # 4 x² + x + 4 = 0 a = 1 b = 1 c = 4 b² - 4ac (1) ² - 4(1)(4) 1 – 16 -15 Negative To check, solve for the roots. X = X = X =   X =   Two Different Imaginary Numbers

9. CHALLENGE x² - 5x + 6 = 0 a = 1 b = -5 c = 6 b² - 4ac (-5) ² - 4(1)(6) 25 – 24 1 Positive and a Perfect Square To check, solve for the roots. X = X = X =   X = X = 6/2 x = 4/2 X = 3 x = 2   Two Different Rational Numbers

10. RELATIONSHIP BETWEEN THE COEFFICIENT OF QUADRATIC EQUATION

11. SUM OF THE ROOTS r1 + r2 = -b/a

12. Example # 1 x² - 5x + 6 = 0 a = 1 b = -5 c = 6 r1 + r2 = -b/a r1 + r2 = -(-5)/1 r1 + r2 = 5/1 5 Sum of the Roots To check, solve for the roots. X = X = X = X =   X = X = 6/2 x = 4/2 X = 3 x = 2   X =   5

13. Example # 2 2x² + 2x - 12 = 0 a = 2 b = 2 c = -12 r1 + r2 = -b/a r1 + r2 = -(2)/2 r1 + r2 = -2/2 -1 Sum of the Roots To check, solve for the roots. X = X = X = X =   X = X = 8/4 x = -12/4 X = 2 x = -3   X =   -1

14. PRODUCT OF THE ROOTS r1 * r2 = c/a

15. Example # 1 x² - 5x + 6 = 0 a = 1 b = -5 c = 6 r1 * r2 = c/a r1 * r2 = 6/1 r1 * r2 = 6/1 6 Product of the Roots To check, solve for the roots. X = X = X = X =   X = X = 6/2 x = 4/2 X = 3 x = 2   X =   6

16. Example # 2 2x² + 2x - 12 = 0 a = 2 b = 2 c = -12 r1 * r2 = c/a r1 * r2 = -12/2 r1 * r2 = -12/2 -6 Product of the Roots To check, solve for the roots. X = X = X = X =   X = X = 8/4 x = -12/4 X = 2 x = -3   X =   -6

17. CHALLENGE: 3x² + 15x + 12 = 0 a = 3 b = 15 c = 12 r1 + r2 = -b/a r1 + r2 = -(15)/3 r1 + r2 = -15/3 -5 Sum of the Roots r1 * r2 = c/a r1 * r2 = 12/3 r1 +* r2 = 12/3 4 Product of the Roots

18. CHALLENGE 3x² + 15x + 12 = 0 a = 3 b = 15 c = 12 To check, solve for the roots. X = X = X = X =   X = X = -6/6 x = -24/6 X = -1 x = -4   X =   -1 + (-4) = -5 (-1 )(-4) = 4