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

JEE Advanced Mathematics question

If the equations and have a common root then the rational values of and are

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

The roots of are , irrational conjugates. If are rational, the second quadratic has rational coefficients, so if it has one of these irrational roots it also has the conjugate. Thus both roots are common and the coefficients

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Question ID VK-110056