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For the quadratic equation \(x^2-(u+6)x+6u=0\) to have equal roots, what must be the value of \(u\)?
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Answer and explanation
Correct answer: \(u=6\)
Equal roots require the discriminant to be zero. Here, \(a=1\), \(b=-(u+6)\), and \(c=6u\). Thus, \(D=b^2-4ac=(u+6)^2-24u=(u-6)^2\). Setting \(D=0\) gives \(u=6\). Exam tip: For equal roots, immediately apply the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(u=6\)
Why is this the correct answer?
Equal roots require the discriminant to be zero. Here, \(a=1\), \(b=-(u+6)\), and \(c=6u\). Thus, \(D=b^2-4ac=(u+6)^2-24u=(u-6)^2\). Setting \(D=0\) gives \(u=6\). 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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