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JEE Main Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main

Consider the following statements: 1. The equation and have common root and second equation has equal roots if . 2. If is a root of , then the other root is . 3. The expression is positive for all real values of . Which of these is/are correct?

Answer: (C)

Solution

(1) Equal roots of need , and the root is ; it satisfies , so , i.e. , so is true. (2) From we get

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Question ID VK-013719