Question

find the value of k of the quadratic equation x²-k(4x-k+1)+2 =0 given that it has equal roots​

Answer 1

For equal roots , D = 0

x²-k(4x-k+1)+2 = 0

x²-4kx+k²-k+2 = 0

a = 1 , b = -4 , c= k²-k+2

D = b²-4ac

b²-4ac = 0

(-4)²-4(1)(k²-k+2) = 0

16 - 4k²+k-8 = 0

8-4k²+k = 0

4k²-k = 8

4k(k-1) = 8

4k = 8 , (k-1) = 8

k = 2 , k = 9

Hope it helps!!

Thank you ✌️

Answer 2

$\huge\red{Answer}$

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For equal roots , D = 0

x²-k(4x-k+1)+2 = 0

x²-4kx+k²-k+2 = 0

a = 1 , b = -4 , c= k²-k+2

D = b²-4ac

b²-4ac = 0

(-4)²-4(1)(k²-k+2) = 0

16 - 4k²+k-8 = 0

8-4k²+k = 0

4k²-k = 8

4k(k-1) = 8

4k = 8 , (k-1) = 8

k = 2 , k = 9

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