2022 · Q42
Consider a question and two statements : Question : Does the equation ax² + bx + c = 0 have real roots of opposite sign?Statement - I : The discriminant D > 0Statement - II : (c)/(a) > 0Which one of the following is correct in respect of the question and the statements?
Elementary MathematicsAlgebra
- AStatement - I alone is sufficient to answer the question
- BStatement - II alone is sufficient to answer the question
- CBoth Statement - I and Statement - II are together sufficient to answer the question
- DBoth Statement - I and Statement - II are not sufficient to answer the question
Explanation
Opposite-sign real roots are equivalent to c/a < 0 (which also forces D > 0). Statement I alone leaves the sign unknown; statement II alone gives the same sign if real. Together, D > 0 and c/a > 0 mean real roots of the same sign - definitely not opposite - so the question is answered. Hence the keyed option is C.