A student claims that the equation \(x^2+(m-4)x+m=0\) will have equal real roots only for \(m=4\), because the coefficient of \(x\) becomes zero. Which is the correct evaluation of this claim?
Answer and explanation
Correct answer: The claim is incorrect; equal real roots occur for \(m=6\pm2\sqrt{5}\)
Equal roots require the discriminant to be zero. Here, \(D=(m-4)^2-4m=m^2-12m+16\). Setting \(D=0\) gives \(m=6\pm2\sqrt5\). At \(m=4\), \(D=-16\), so there are no real roots. Exam tip: never decide the nature of roots merely from the coefficient of \(x\).
Frequently asked questions
What is the correct answer to this question?
The claim is incorrect; equal real roots occur for \(m=6\pm2\sqrt{5}\)
Why is this the correct answer?
Equal roots require the discriminant to be zero. Here, \(D=(m-4)^2-4m=m^2-12m+16\). Setting \(D=0\) gives \(m=6\pm2\sqrt5\). At \(m=4\), \(D=-16\), so there are no real roots. Exam tip: never decide the nature of roots merely from the coefficient of \(x\).
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.
