If the quadratic equation \(3x^2+mx+12=0\) has equal roots, what are the possible values of \(m\)?
Answer and explanation
Correct answer: \(m=12\) or \(m=-12\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=3\), \(b=m\), and \(c=12\), so \(m^2-4(3)(12)=0\). Therefore, \(m^2=144\), giving \(m=\pm12\), that is, \(m=12\) or \(m=-12\). Option B would give \(m^2=36\), which does not satisfy the required condition. Exam tip: For equal-root questions, start by setting the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(m=12\) or \(m=-12\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=3\), \(b=m\), and \(c=12\), so \(m^2-4(3)(12)=0\). Therefore, \(m^2=144\), giving \(m=\pm12\), that is, \(m=12\) or \(m=-12\). Option B would give \(m^2=36\), which does not satisfy the required condition. Exam tip: For equal-root questions, start by setting the discriminant equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
