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What is the condition for the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), to have two equal real roots?
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Answer and explanation
Correct answer: \(b^2-4ac=0\)
The discriminant is \(D=b^2-4ac\). If \(D=0\), the formula gives the same value \(x=\frac{-b}{2a}\) twice, so the roots are equal. In contrast, \(D>0\) gives distinct real roots. Exam tip: check the discriminant sign first.
Frequently asked questions
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 \(D=0\), the formula gives the same value \(x=\frac{-b}{2a}\) twice, so the roots are equal. In contrast, \(D>0\) gives distinct real roots. Exam tip: check the discriminant sign first.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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