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When will the two roots of the equation \(x^2-(m+n)x+mn=0\) be equal?
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Answer and explanation
Correct answer: \(m=n\)
A quadratic equation has equal real roots when its discriminant is zero. Here, \(D=(m+n)^2-4mn=m^2-2mn+n^2=(m-n)^2\). Thus \((m-n)^2=0\), which gives \(m=n\). Exam tip: For equal-root questions, begin by setting the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(m=n\)
Why is this the correct answer?
A quadratic equation has equal real roots when its discriminant is zero. Here, \(D=(m+n)^2-4mn=m^2-2mn+n^2=(m-n)^2\). Thus \((m-n)^2=0\), which gives \(m=n\). Exam tip: For equal-root questions, begin by setting the discriminant equal to zero.
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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