If a and b are real constants, when will the two roots of \(x^2-(a+b)x+ab=0\) be equal?
Answer and explanation
Correct answer: \(a=b\)
A quadratic equation has equal roots when its discriminant is zero. Here, \(D=(a+b)^2-4ab=a^2-2ab+b^2=(a-b)^2\). Since a and b are real, \((a-b)^2=0\) only when \(a=b\). Therefore, option A is correct. Exam tip: set \(D=0\) first; conditions such as \(a+b=0\) or \(ab=1\) do not generally imply equal roots.
Frequently asked questions
What is the correct answer to this question?
\(a=b\)
Why is this the correct answer?
A quadratic equation has equal roots when its discriminant is zero. Here, \(D=(a+b)^2-4ab=a^2-2ab+b^2=(a-b)^2\). Since a and b are real, \((a-b)^2=0\) only when \(a=b\). Therefore, option A is correct. Exam tip: set \(D=0\) first; conditions such as \(a+b=0\) or \(ab=1\) do not generally imply equal roots.
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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