First slide
Theory of equations
Question

If the equations 4x2x1=0 and 3x2+(λ+μ)x+λμ=0 have a root common, then the rational values of λ and μ are

Moderate
Solution

Roots of 4x2x1=0 are irrational. So, one root common implies both roots are common. Therefore,

43=1λ+μ=1λμ λ=34,μ=0

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