For which values of \(\mu\) will the roots of the quadratic equation \(x^2-2\mu x+2\mu=0\) be equal?
Answer and explanation
Correct answer: \(\mu=0\) or \(\mu=2\)
Here, \(a=1\), \(b=-2\mu\), and \(c=2\mu\). A quadratic equation has equal roots when its discriminant \(D=b^2-4ac\) is zero. Thus, \(D=4\mu^2-8\mu=4\mu(\mu-2)=0\), giving \(\mu=0\) or \(\mu=2\). Hence, option A is correct. Choosing only \(\mu=2\) or only \(\mu=0\) omits one valid value. Exam tip: For equal roots, set the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(\mu=0\) or \(\mu=2\)
Why is this the correct answer?
Here, \(a=1\), \(b=-2\mu\), and \(c=2\mu\). A quadratic equation has equal roots when its discriminant \(D=b^2-4ac\) is zero. Thus, \(D=4\mu^2-8\mu=4\mu(\mu-2)=0\), giving \(\mu=0\) or \(\mu=2\). Hence, option A is correct. Choosing only \(\mu=2\) or only \(\mu=0\) omits one valid value. Exam tip: For equal roots, set 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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