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Question

Find a quadratic equation whose product of roots x1 and x2 is equal to 4 and satisfying the relation x1x11+x2x21=2.

A
x22x+4=0
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B
x23x+4=0
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C
x22x+3=0
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D
x23x+2=0
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Solution

The correct option is B x22x+4=0
Simplifying the expression, we get
x1.x2x1+x2x1x2=2(x1x2(x1x2)+1)
2(x1.x2)(x1+x2)=2x1x22(x1+x2)+2
x1+x2=2
And x1.x2=4
Hence, the required equation with roots x1 and x2 is
x22x+4=0.

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