For the quadratic equation \(x^2-(s+4)x+4s=0\), what must be the value of \(s\) for its roots to be equal?
Answer and explanation
Correct answer: \(s=4\)
Here, \(a=1\), \(b=-(s+4)\), and \(c=4s\). Equal roots require the discriminant \(D=b^2-4ac\) to be zero. Thus, \(D=(s+4)^2-16s=s^2-8s+16=(s-4)^2\). Therefore, \((s-4)^2=0\), giving \(s=4\). The distractor \(s=0\) is incorrect because it gives \(D=16\), not zero. Exam tip: for equal roots, immediately apply the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(s=4\)
Why is this the correct answer?
Here, \(a=1\), \(b=-(s+4)\), and \(c=4s\). Equal roots require the discriminant \(D=b^2-4ac\) to be zero. Thus, \(D=(s+4)^2-16s=s^2-8s+16=(s-4)^2\). Therefore, \((s-4)^2=0\), giving \(s=4\). The distractor \(s=0\) is incorrect because it gives \(D=16\), not zero. Exam tip: for equal roots, immediately apply 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
