Which of the following equations has no real roots?
Answer and explanation
Correct answer: x² + 2x + 5 = 0
For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² − 4ac. In option (A), D = 2² − 4(1)(5) = −16. Since D < 0, the equation has no real roots. In option (D), D = 0, so it has one repeated real root, while options (B) and (C) have D > 0. Exam tip: Check the sign of the discriminant first to determine the nature of the roots.
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What is the correct answer to this question?
x² + 2x + 5 = 0
Why is this the correct answer?
For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² − 4ac. In option (A), D = 2² − 4(1)(5) = −16. Since D < 0, the equation has no real roots. In option (D), D = 0, so it has one repeated real root, while options (B) and (C) have D > 0. Exam tip: Check the sign of the discriminant first to determine the nature of the roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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