For a quadratic equation with real coefficients, if the discriminant \(D<0\), what is the nature of its roots?
Answer and explanation
Correct answer: No real roots; two non-real complex roots
The discriminant is \(D=b^2-4ac\). When \(D<0\), the root formula contains \(\sqrt{D}\), the square root of a negative number. Hence, there are no real roots; the roots form a complex conjugate pair. Exam tip: \(D>0\) gives two distinct real roots.
Frequently asked questions
What is the correct answer to this question?
No real roots; two non-real complex roots
Why is this the correct answer?
The discriminant is \(D=b^2-4ac\). When \(D<0\), the root formula contains \(\sqrt{D}\), the square root of a negative number. Hence, there are no real roots; the roots form a complex conjugate pair. Exam tip: \(D>0\) gives two distinct 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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