If the equation `4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0` have a root common, then the irrational values of `lambda and mu` are a `lambda=(-3)/4` b. `lambda=0` c. `mu=3/4` b.`mu=0`

Options

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)`

Answer

C

Explanation

`(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`