Which equation has discriminant −11?
Answer and explanation
Correct answer: x² + x + 3 = 0
For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² − 4ac. For option A, a = 1, b = 1 and c = 3, so D = 1² − 4(1)(3) = 1 − 12 = −11. Therefore option A exactly matches the required discriminant. The remaining choices can be checked to rule them out: option B gives D = 3² − 4(1)(1) = 9 − 4 = 5; option C gives D = 1² − 4(2)(2) = 1 − 16 = −15; and option D gives D = (−4)² − 4(1)(10) = 16 − 40 = −24. Thus only option A has discriminant −11. Its negative discriminant also indicates that its roots are non-real complex conjugates.
Frequently asked questions
What is the correct answer to this question?
x² + x + 3 = 0
Why is this the correct answer?
For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² − 4ac. For option A, a = 1, b = 1 and c = 3, so D = 1² − 4(1)(3) = 1 − 12 = −11. Therefore option A exactly matches the required discriminant. The remaining choices can be checked to rule them out: option B gives D = 3² − 4(1)(1) = 9 − 4 = 5; option C gives D = 1² − 4(2)(2) = 1 − 16 = −15; and option D gives D = (−4)² − 4(1)(10) = 16 − 40 = −24. Thus only option A has discriminant −11. Its negative discriminant also indicates that its roots are non-real complex conjugates.
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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