Exercixe - 6
Solve the following quadratic equation:
1. x2 - x - 20 = 0 3. 6x2 + 31x + 40 = 0 5. 16x2 - 24x = 0 7. 9. abx2 +(b2 - ac) x - bc = 0 |
2. 9x2 - 3x - 2 = 0 4. x2 + 6x + 5 = 0 6. 25x2 - 30x + 9 = 0 8. 10. x2 - 4qx + 4q2 = 0 |
Determine whether the following quadratic equations have real roots and if they have find them:
11. 13. 15. 17. 19. |
12. 14. x2 + 3x + 1 = 0 16. 18. 20. |
Find the value of k. If the following quadratic equation has equal roots:
21. k2x2 - 2(2k - 1) x + 4 = 0
22. x2 - 2kx + 7k - 12 = 0
23. ( k + 1) x2 - 2(k - 1) x + 1 = 0
24. If the equation (1 + m2) x2 + 2 mcx + (c2 - a2) = 0 has equal roots, prove that c2 = a2(1 + m2)
25. If the roots of the equation (a - b) x2 + (b - c) x + (c - a) = 0 are equal, prove that 2a = b + c.
Find the value of p for which the following equations has real roots:
26.2x2 + px + 8 = 0
27. 3x2 + 3x + p = 0
28. 5px2 - 8x + 2 = 0
| Answers | ||
1. -4, 5 4. -1, -5 7. -1 10. 2q 13. -9, 7 16. 19. 22. 3, 4 27. |
2. -1/3, 2/3 5. 0, 3/2 8. -2 11. 5, 5/2 14. 17. 20. 23. 0, 3 28. |
3. -1/2, 2/3 6. 3/5, 3/5 9. c/b, - b/a 12. 2, -5 15. No real roots.
18. 21. 1/4 26. |
| Subjects | Maths (Part-1) by Mr. M. P. Keshari |
| Chapter 1 | Linear Equations in Two Variables |
| Chapter 2 | HCF and LCM |
| Chapter 3 | Rational Expression |
| Chapter 4 | Quadratic Equations |
| Chapter 5 | Arithmetic Progressions |
| Chapter 6 | Instalments |
| Chapter 7 | Income Tax |
| Chapter 8 | Similar Triangles |
