Which value of \(q\) is required for the two roots of the quadratic equation \(2x^2-(q+4)x+2q=0\) to be equal?
Answer and explanation
Correct answer: Only \(q=4\)
For the equation, \(a=2\), \(b=-(q+4)\), and \(c=2q\). Equal roots require the discriminant \(D=b^2-4ac\) to be zero. Thus, \(D=(q+4)^2-16q=q^2-8q+16=(q-4)^2\). Setting this equal to zero gives \(q=4\). The values in option B do not make the discriminant zero. Exam tip: For equal roots, immediately apply the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
Only \(q=4\)
Why is this the correct answer?
For the equation, \(a=2\), \(b=-(q+4)\), and \(c=2q\). Equal roots require the discriminant \(D=b^2-4ac\) to be zero. Thus, \(D=(q+4)^2-16q=q^2-8q+16=(q-4)^2\). Setting this equal to zero gives \(q=4\). The values in option B do not make the discriminant zero. 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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