Question

1. Find the values of k for which the quadratic equation k²x² - 2(k – 1)x + 4 = 0 has real and equal
roots.
(a) k = 0 or k =1/3 (b)k – 1 or k = 1/3 (c)k=-1 or k = 1/3 (d) k =-3 or k=1/3
please send the solution fast please ​

Answer 1

Answer:

(c) k = - 1, k = 1/3

Step-by-step explanation:

1). m² - n² = (m - n)(m + n)

2). Quadratic equation ax² + bx + c = 0 has equal roots if D = b² - 4ac = 0

~~~~~~~

k²x² - 2(k - 1)x + 4 = 0

a = k² , b = - 2(k - 1) , c = 4

D = [- 2(k - 1)]² - 4×4×k² = 0

[2(k - 1)]² - (4k)² = 0

(2(k - 1) + 4k)(2(k - 1) - 4k) = 0

2k - 2 + 4k = 0 ⇒ k = 1/3

2k - 2 - 4k = 0 ⇒ k = - 1