If the quadratic equation \(4x^2+mx+1=0\) has equal roots, what are the possible values of \(m\)?
Answer and explanation
Correct answer: \(m=4\) or \(m=-4\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=4\), \(b=m\), and \(c=1\), so \(D=m^2-16=0\). Therefore, \(m^2=16\), giving \(m=4\) or \(m=-4\). Choosing only \(m=4\) is incomplete because the negative value also produces equal roots. Exam tip: For equal-root questions, set \(b^2-4ac=0\) directly.
Frequently asked questions
What is the correct answer to this question?
\(m=4\) or \(m=-4\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=4\), \(b=m\), and \(c=1\), so \(D=m^2-16=0\). Therefore, \(m^2=16\), giving \(m=4\) or \(m=-4\). Choosing only \(m=4\) is incomplete because the negative value also produces equal roots. Exam tip: For equal-root questions, set \(b^2-4ac=0\) directly.
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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