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Question

On Solving the following quadratic equation by factorization, the roots are a2+b23,b2a23:
9x26b2x(a4b4)=0

A
True
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B
False
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Solution

The correct option is A True
9x26b2x(a4b4)=0
9x23(2b2)x(a4b4)=0
9x23(b2a2+b2+a2)x+(b4a4)=0
9x23(b2a2)x3(b2+a2)x+(b2+a2)(b2a2)=0
3x(3xb2+a2)(b2+a2)(3xb2+a2)=0
(3xb2a2)(3xb2+a2)=0
3xb2a2=0 and 3xb2+a2=0
3x=a2+b2 and 3x=b2a2
x=a2+b23 and x=b2a23
Roots given in question are correct.

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