InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the values of k for which the roots are real and equal in each of the following equations:(i) kx2 + 4x + 1 = 0(ii) \(kx^2-2\sqrt{5}+4=0\) (iii) 3x2 - 5x + 2k = 0(iv) 4x2 + kx + 9 = 0(v) 2kx2 - 40x + 25 = 0 |
|
Answer» (i) kx2 + 4x + 1 = 0 For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D = 0, roots are real and equal kx2 + 4x + 1 = 0 ⇒ D = 16 – 4k = 0 ⇒ k = 4 (ii) \(kx^2-2\sqrt{5}x+4=0\) For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D = 0, roots are real and equal \(kx^2-2\sqrt{5}x+4=0\) ⇒ D = 4 × 5 – 4 × 4k = 0 ⇒ k = 5/4 (iii) 3x2 - 5x + 2k = 0 For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D = 0, roots are real and equal 3x2 - 5x + 2k = 0 ⇒ D = 25 – 4 × 3 × 2k = 0 ⇒ k = 25/24 (iv) 4x2 + kx + 9 =0 For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D = 0, roots are real and equal 4x2 + kx + 9 =0 ⇒ D = k2 – 4 × 4 × 9 = 0 ⇒ k2 – 144 = 0 ⇒ k = 12 (v) 2kx2 - 40x + 25 = 0 For a quadratic equation, ax2 + bx + c = 0 D = b2 – 4ac If D = 0, roots are real and equal 2kx2 - 40x + 25 = 0 ⇒ 1600 – 4 × 2k × 25 = 0 ⇒ k = 8 |
|