If the equation \(x^2-2(k-1)x+k+1=0\) has equal roots, what are the values of \(k\)?
Answer and explanation
Correct answer: \(k=0\) or \(k=3\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=-2(k-1)\), and \(c=k+1\). Thus, \(D=4(k-1)^2-4(k+1)=4(k^2-3k)=4k(k-3)\). Setting \(D=0\) gives \(k=0\) or \(k=3\), so option A is correct. Exam tip: whenever a quadratic equation has equal roots, begin by applying \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(k=0\) or \(k=3\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=-2(k-1)\), and \(c=k+1\). Thus, \(D=4(k-1)^2-4(k+1)=4(k^2-3k)=4k(k-3)\). Setting \(D=0\) gives \(k=0\) or \(k=3\), so option A is correct. Exam tip: whenever a quadratic equation has equal roots, begin by applying \(D=0\).
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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