For what value of \(k\) will the quadratic equation \(2x^2-(k+4)x+2k=0\) have equal roots?
Answer and explanation
Correct answer: \(k=4\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=2\), \(b=-(k+4)\), and \(c=2k\). Thus, \(D=(k+4)^2-16k=k^2-8k+16=(k-4)^2\). Setting this equal to zero gives \(k=4\). The other values do not make the discriminant zero. Exam tip: equal roots in a quadratic equation always require \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(k=4\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=2\), \(b=-(k+4)\), and \(c=2k\). Thus, \(D=(k+4)^2-16k=k^2-8k+16=(k-4)^2\). Setting this equal to zero gives \(k=4\). The other values do not make the discriminant zero. Exam tip: equal roots in a quadratic equation always require \(D=0\).
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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