Question

find value of k for which x2 - (k+1)x +4=0 has equal roots​

Answer 1

x² - (k +1)x + 4 = 0

It is given that Discriminant ( D ) = 0

As it has equal roots

Now, D = b² - 4ac

where a = 1 , b = -(k +1) and c = 4

0 = (-(k+1))² - 4(1)(4)

0 = k² + 2k + 1 - 16

k² + 2k + 1 = 0 + 16

k² + 2k = 16 - 1

k² + 2k = 15

k² + 2k - 15 = 0

k² + (5 - 3)k - 15 = 0

k² + 5k - 3k - 15 = 0

k ( k + 5) - 3 (k + 5) = 0

(k - 3) (k +5) = 0

k - 3 = 0 or k + 5 = 0

Therefore

k = 3 or k = (-5)

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