If the quadratic equation \(x^2+kx+25=0\) has equal roots, what are the possible values of \(k\)?
Answer and explanation
Correct answer: \(k=10\) or \(k=-10\)
For equal roots, the discriminant \(\Delta=b^2-4ac\) must be zero. Here, \(a=1, b=k, c=25\), so \(\Delta=k^2-4(1)(25)=k^2-100\). Thus, \(k^2-100=0\), giving \(k=\pm10\), or \(k=10\) and \(k=-10\). For the closest distractor, \(k=\pm5\) gives a discriminant of \(-75\), so the roots are not equal real roots. Exam tip: For equal roots, immediately use \(b^2-4ac=0\).
Frequently asked questions
What is the correct answer to this question?
\(k=10\) or \(k=-10\)
Why is this the correct answer?
For equal roots, the discriminant \(\Delta=b^2-4ac\) must be zero. Here, \(a=1, b=k, c=25\), so \(\Delta=k^2-4(1)(25)=k^2-100\). Thus, \(k^2-100=0\), giving \(k=\pm10\), or \(k=10\) and \(k=-10\). For the closest distractor, \(k=\pm5\) gives a discriminant of \(-75\), so the roots are not equal real roots. Exam tip: For equal roots, immediately use \(b^2-4ac=0\).
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.
