For which values of \(k\) will the quadratic equation \(x^2-2(k-5)x+36=0\) have equal roots?
Answer and explanation
Correct answer: \(k=11\) or \(k=-1\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=-2(k-5)\), and \(c=36\). Thus, \(D=4(k-5)^2-144=0\), which gives \((k-5)^2=36\). Therefore, \(k-5=\pm6\), so \(k=11\) or \(k=-1\). Exam tip: For equal roots of a quadratic equation, set the discriminant directly equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(k=11\) or \(k=-1\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=-2(k-5)\), and \(c=36\). Thus, \(D=4(k-5)^2-144=0\), which gives \((k-5)^2=36\). Therefore, \(k-5=\pm6\), so \(k=11\) or \(k=-1\). Exam tip: For equal roots of a quadratic equation, set the discriminant directly 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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