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Which condition identifies that the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), has two equal real roots?
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Answer and explanation
Correct answer: \(b^2-4ac=0\)
When the discriminant \(D=b^2-4ac\) is zero, \(\sqrt{D}=0\) in \(\frac{-b\pm\sqrt{D}}{2a}\), so both roots are equal. For \(D>0\), the roots are distinct. Exam tip: equal roots always mean \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(b^2-4ac=0\)
Why is this the correct answer?
When the discriminant \(D=b^2-4ac\) is zero, \(\sqrt{D}=0\) in \(\frac{-b\pm\sqrt{D}}{2a}\), so both roots are equal. For \(D>0\), the roots are distinct. Exam tip: equal roots always mean \(D=0\).
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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