Question

`If the equation 4x^2 - 2 (k + 1) + (k + 1) = 0 Find the value of k.​​

Answer 1

Answer:

For real and equal roots,

D = 0

b² - 4ac = 0

Here,

a = 4

b = -2(k + 1)

c = (k + 1)

=>  -2²(k + 1)² - 4 x 4 x (k + 1) = 0

=> 4(k² + 2k + 1) - 16(k + 1) = 0

=>4k² + 8k + 4 - 16k - 16 = 0

=> 4k² - 8k - 12 = 0

=> k² - 2k - 3 = 0

=> k² -3k + k - 3 = 0

=> k(k - 3) + 1(k - 3) = 0

=> (k + 1)(k - 3) = 0

k = -1 or k = 3

∴ The values of k are -1 and 3

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