If the equations `4x^(2)-x-1=0` and `3x^(2)+(lambda+mu)x+lambda-mu=0` have a root common, then the rational values of `lambda` and `mu` are

Monjur Alahi

If the equations `4x^(2)-x-1=0` and `3x^(2)+(lambda+mu)x+lambda-mu=0` have a root common, then the rational values of `lambda` and `mu` are
A. `lambda=0`, `mu=(-3)/(4)`
B. `lambda=(-3)/(4)`, `mu=(3)/(4)`
C. `lambda=(-3)/(4)`, `mu=0`
D. `lambda=(-3)/(4)`, `mu=(1)/(4)`


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Salim Ahmed Kawsar

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Correct Answer - C
`(c )` Roots of `4x^(2)-x-1=0` are irrational.
So, one root common implies both roots are common.
`:. (4)/(3)=(-1)/(lambda+mu)=(-1)/(lambda-mu)=(-2)/(2lambda)=(0)/(2mu)`
So, `lambda=(-3)/(4)`, `mu=0`

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