If the two roots of \(2x^2+mx+18=0\) are equal, what are the possible values of \(m\)?
Answer and explanation
Correct answer: \(m=12\) or \(m=-12\)
For a quadratic equation \(ax^2+bx+c=0\) to have equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=2\), \(b=m\), and \(c=18\), so \(m^2-4(2)(18)=0\), giving \(m^2=144\). Therefore, \(m=\pm12\), or \(m=12\) or \(m=-12\). Option B results from an incorrect calculation of \(4ac\). Exam tip: whenever equal roots are mentioned, immediately use \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(m=12\) or \(m=-12\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\) to have equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=2\), \(b=m\), and \(c=18\), so \(m^2-4(2)(18)=0\), giving \(m^2=144\). Therefore, \(m=\pm12\), or \(m=12\) or \(m=-12\). Option B results from an incorrect calculation of \(4ac\). Exam tip: whenever equal roots are mentioned, immediately use \(D=0\).
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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