For which values of \(\lambda\) does the equation \(x^2-2\lambda x+\lambda=0\) have equal roots?
Answer and explanation
Correct answer: \(\lambda=0\) or \(\lambda=1\)
A quadratic equation has equal roots when its discriminant is zero. Here, \(a=1\), \(b=-2\lambda\), and \(c=\lambda\), so \(D=b^2-4ac=4\lambda^2-4\lambda=4\lambda(\lambda-1)\). Setting \(D=0\) gives \(\lambda=0\) or \(\lambda=1\). Hence, option A is correct. Option B is incomplete because it omits \(\lambda=0\). Exam tip: For equal roots, immediately apply the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(\lambda=0\) or \(\lambda=1\)
Why is this the correct answer?
A quadratic equation has equal roots when its discriminant is zero. Here, \(a=1\), \(b=-2\lambda\), and \(c=\lambda\), so \(D=b^2-4ac=4\lambda^2-4\lambda=4\lambda(\lambda-1)\). Setting \(D=0\) gives \(\lambda=0\) or \(\lambda=1\). Hence, option A is correct. Option B is incomplete because it omits \(\lambda=0\). Exam tip: For equal roots, immediately apply the condition \(D=0\).
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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