If the equations 4x2−x−1=0 and 3x2+(λ+μ)x+λ−μ=0 have a root common, then the rational values of λ and μ are

Roots of 4x2−x−1=0 are irrational. So, one root common implies both roots are common. Therefore,43=−1λ+μ=−1λ−μ⇒ λ=−34,μ=0