For which value of \(n\) will the equation \(x^2+(n+2)x+2n=0\) have equal roots?
Answer and explanation
Correct answer: \(n=2\)
A quadratic equation \(ax^2+bx+c=0\) has equal roots when its discriminant \(D=b^2-4ac\) is zero. Here, \(a=1\), \(b=n+2\), and \(c=2n\), so \(D=(n+2)^2-8n=n^2-4n+4=(n-2)^2\). Thus, \((n-2)^2=0\), giving \(n=2\). Substitution produces \(x^2+4x+4=0\), or \((x+2)^2=0\), confirming equal roots. Exam tip: For equal-root questions, set the discriminant equal to zero first.
Frequently asked questions
What is the correct answer to this question?
\(n=2\)
Why is this the correct answer?
A quadratic equation \(ax^2+bx+c=0\) has equal roots when its discriminant \(D=b^2-4ac\) is zero. Here, \(a=1\), \(b=n+2\), and \(c=2n\), so \(D=(n+2)^2-8n=n^2-4n+4=(n-2)^2\). Thus, \((n-2)^2=0\), giving \(n=2\). Substitution produces \(x^2+4x+4=0\), or \((x+2)^2=0\), confirming equal roots. Exam tip: For equal-root questions, set the discriminant equal to zero first.
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.
