If the quadratic equation \(x^2-2mx+3m=0\) has real and equal roots, what are the possible values of \(m\)?
Answer and explanation
Correct answer: \(m=0\) या \(m=3\)
For a quadratic equation to have real and equal roots, its discriminant must be zero. Here, \(a=1\), \(b=-2m\), and \(c=3m\), so \(D=b^2-4ac=(-2m)^2-4(1)(3m)=4m(m-3)\). Setting \(D=0\) gives \(m=0\) or \(m=3\). Both values are valid because the coefficient of \(x^2\) remains non-zero. Exam tip: For equal real roots, immediately use the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(m=0\) या \(m=3\)
Why is this the correct answer?
For a quadratic equation to have real and equal roots, its discriminant must be zero. Here, \(a=1\), \(b=-2m\), and \(c=3m\), so \(D=b^2-4ac=(-2m)^2-4(1)(3m)=4m(m-3)\). Setting \(D=0\) gives \(m=0\) or \(m=3\). Both values are valid because the coefficient of \(x^2\) remains non-zero. Exam tip: For equal real roots, immediately use 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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