Math, asked by ishitasinghai, 5 months ago

If x² + k (4x + k -1) +2 =0 has equal roots, then find the value of k?​

Answers

Answered by kirtipadhi06
2

Answer:

Given equation is -

x² + k (4x + k -1) +2 =0

=> x²+ 4kx+ k²- k+2 = 0

Here,

a = 1 \\ b = 4k \\ and \: c =  {k}^{2}  - k + 2

For real and equal roots ,

D=0

D =  \sqrt{b²-4ac}

 =  >  \sqrt{ (4k)²-4(1)(k²-k+2)} = 0

 =  > 16k²-4(k²-k+2)=0

 =  > 4k²-k²+k-2=0

 =  > 3k²+k-2=0

 =  > 3k²+3k-2k-2=0

 =  > 3k(k+1)-2(k+1)=0

 =  > (3k-2)(k+1)=0

So, k =  \frac{2}{3}  \:  or \:  k = -1

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