If the coefficients of a quadratic equation are rational and its discriminant is D = 12, what is the nature of its roots?
Answer and explanation
Correct answer: Two real irrational and distinct
For a quadratic equation, D = b² − 4ac. Since D = 12 is positive, the roots are real and distinct. Also, 12 is not a perfect square and the coefficients are rational, so the roots are irrational. Hence, option A is correct. Exam tip: D > 0 gives distinct real roots, D = 0 gives equal roots, and D < 0 gives no real roots.
Frequently asked questions
What is the correct answer to this question?
Two real irrational and distinct
Why is this the correct answer?
For a quadratic equation, D = b² − 4ac. Since D = 12 is positive, the roots are real and distinct. Also, 12 is not a perfect square and the coefficients are rational, so the roots are irrational. Hence, option A is correct. Exam tip: D > 0 gives distinct real roots, D = 0 gives equal roots, and D < 0 gives no real 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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