Statement 1: If equations ax^2+bx+c=0, (a,b,c R) and 2x^2+3x+4=0 have a common root, then a:b:c=2:3:4. Statement 2: Roots of 2x^2+3x+4=0 are imaginary.

JEE Main Mathematics question

Statement 1: If equations , and have a common root, then . Statement 2: Roots of are imaginary.

(A)Assertion is True, Reason is True; Reason is correct explanation for AssertionCorrect
(B)Assertion is True, Reason is True; Reason is not correct explanation for Assertion
(C)Assertion is True, Reason is False
(D)Assertion is False, Reason is True

Answer: (A)

Solution

The discriminant of is , so its roots are non-real conjugates and Statement 2 is true. A real-coefficient quadratic that shares one non-real root with it also has the conjugate root, so both roots are

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Question ID VK-013774