If the roots of the quadratic equation \(x^2-2mx+36=0\) are equal, what are the possible values of \(m\)?
Answer and explanation
Correct answer: \(m=\pm6\)
For equal roots, the discriminant must be zero. Here, \(a=1\), \(b=-2m\), and \(c=36\), so \(D=b^2-4ac=(-2m)^2-4(1)(36)=4m^2-144\). Setting \(D=0\) gives \(4m^2-144=0\), hence \(m^2=36\) and \(m=\pm6\). Choosing only \(m=6\) or only \(m=-6\) omits one valid possibility. Exam tip: whenever the roots are equal, set the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(m=\pm6\)
Why is this the correct answer?
For equal roots, the discriminant must be zero. Here, \(a=1\), \(b=-2m\), and \(c=36\), so \(D=b^2-4ac=(-2m)^2-4(1)(36)=4m^2-144\). Setting \(D=0\) gives \(4m^2-144=0\), hence \(m^2=36\) and \(m=\pm6\). Choosing only \(m=6\) or only \(m=-6\) omits one valid possibility. Exam tip: whenever the roots are equal, set the discriminant equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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