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Question

Find the roots of the given equation 4x2+4bx(a2b2)=0 by the method of completing the square.

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Solution

We have
4x2+4bx(a2b2)=0

x2+bxa2b24=0

x2+2(b2)x+(b2)2=a2b24+(b2)2(x+b2)2=a24

x+b2=±a2x=b2±a2x=ba2,b+a2

Hence, the roots are (a+b2) and (ab2)

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