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For the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), under which condition are its roots non-real?
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Answer and explanation
Correct answer: \(b^2-4ac<0\)
The discriminant is \(D=b^2-4ac\). If \(D<0\), its square root is not real, so the equation has non-real roots. In contrast, \(D=0\) gives equal real roots. Exam tip: determine the nature of roots by checking the sign of \(D\).
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What is the correct answer to this question?
\(b^2-4ac<0\)
Why is this the correct answer?
The discriminant is \(D=b^2-4ac\). If \(D<0\), its square root is not real, so the equation has non-real roots. In contrast, \(D=0\) gives equal real roots. Exam tip: determine the nature of roots by checking the sign of \(D\).
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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