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Question

For what value of k, the equation x2+2(k-4)x+2k=0 has equal roots ?


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Solution

Step 1: Estimate the constants of the equation

The given equation is x2+2(k-4)x+2k=0.

For equal roots,

b2-4ac=0

In this case a=1,b=2k-4,c=2k.

Step 2: Calculate the value of k

Hence,

b2-4ac=0

4k-42-412k=0

4k2-32k+64-8k=0

4k2-40k+64=0

k2-10k+16=0

k2-8k-2k+16=0

kk-8-2k-8=0

k-8k-2=0

k=2,8

Hence, the required values of k are 2 and 8.


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