Which option is correct about the roots of 2x² − 3√2 x + 7 = 0?
Answer and explanation
Correct answer: No real roots (D = −38)
For ax² + bx + c = 0, the discriminant is D = b² − 4ac. In this equation a = 2, b = −3√2, and c = 7. Therefore b² = (−3√2)² = 18, while 4ac = 4 × 2 × 7 = 56. Hence D = 18 − 56 = −38. A negative discriminant means that the quadratic has no real roots; its two roots are complex conjugates. Thus option A is correct. Option B would require D = 0, and options C and D incorrectly use positive discriminant values and therefore claim real roots when the actual discriminant is negative.
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What is the correct answer to this question?
No real roots (D = −38)
Why is this the correct answer?
For ax² + bx + c = 0, the discriminant is D = b² − 4ac. In this equation a = 2, b = −3√2, and c = 7. Therefore b² = (−3√2)² = 18, while 4ac = 4 × 2 × 7 = 56. Hence D = 18 − 56 = −38. A negative discriminant means that the quadratic has no real roots; its two roots are complex conjugates. Thus option A is correct. Option B would require D = 0, and options C and D incorrectly use positive discriminant values and therefore claim real roots when the actual discriminant is negative.
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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