If the discriminants of three quadratic equations are \(D_1=0\), \(D_2=7\), and \(D_3=-2\), respectively, which equation has equal roots?
Answer and explanation
Correct answer: \(D_1=0\)
For a quadratic equation \(ax^2+bx+c=0\), the roots are equal only when the discriminant \(D=b^2-4ac\) is zero. Therefore, the equation with \(D_1=0\) has equal roots. When \(D_2=7>0\), the roots are distinct and real, while \(D_3=-2<0\) gives no real roots. Exam tip: For equal roots, check \(D=0\) directly.
Frequently asked questions
What is the correct answer to this question?
\(D_1=0\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the roots are equal only when the discriminant \(D=b^2-4ac\) is zero. Therefore, the equation with \(D_1=0\) has equal roots. When \(D_2=7>0\), the roots are distinct and real, while \(D_3=-2<0\) gives no real roots. Exam tip: For equal roots, check \(D=0\) directly.
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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