(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