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Find a quadratic equation whose produc...

Find a quadratic equation whose product of roots `x_1 a n d x_2` is equal to 4 and satisfying the relation `(x_1)/(x_1-1)+(x_2)/(x_2-1)=2.`

A

`x^(2)-2x+4=0`

B

`x^(2)-4x+4=0`

C

`x^(2)+2x+4=0`

D

`x^(2)+4x+4=0`

Text Solution

Verified by Experts

The correct Answer is:
A
`:'x_(1)x_(2)=4`……I
and `(x_(1))/(x_(1)-1)+(x_(2))/(x_(2)-1)=2`
`implies2x_(1)x_(2)-x_(1)-x_(2)=2(x_(1)x_(2)-x_(1)-x_(2)+1)`
`implies8-x_(1)-x_(2)=2(4-x_(1)-x_(2)+1)` [from eq. (i)]
or `x_(1)+x_(2)=2`………ii
From Eqs (i) and (ii) required equatioin is
`x^(2)-(x_(1)+x_(2))x+x_(1)x_(2)=0`
or `x^(2)-2x+4=0`
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