For which value of \(k\) will the two roots of the quadratic equation \(2x^2-(k+4)x+2k=0\) be equal?
Answer and explanation
Correct answer: \(k=4\)
Equal roots require the discriminant to be zero. Here \(a=2\), \(b=-(k+4)\), and \(c=2k\), so \(D=b^2-4ac=(k+4)^2-16k=(k-4)^2\). Thus, \((k-4)^2=0\) gives \(k=4\). For example, when \(k=-4\), \(D=64\), so the roots are not equal. Exam tip: For equal roots of a quadratic equation, set \(b^2-4ac=0\).
Frequently asked questions
What is the correct answer to this question?
\(k=4\)
Why is this the correct answer?
Equal roots require the discriminant to be zero. Here \(a=2\), \(b=-(k+4)\), and \(c=2k\), so \(D=b^2-4ac=(k+4)^2-16k=(k-4)^2\). Thus, \((k-4)^2=0\) gives \(k=4\). For example, when \(k=-4\), \(D=64\), so the roots are not equal. Exam tip: For equal roots of a quadratic equation, set \(b^2-4ac=0\).
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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