If the quadratic equation \(x^2+kx+9=0\) has equal roots, which values of \(k\) are possible?
Answer and explanation
Correct answer: \(k=6\) or \(k=-6\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=k\), and \(c=9\), so \(D=k^2-36=0\). Thus, \(k^2=36\), giving \(k=6\) or \(k=-6\). Therefore, option A is correct. Exam tip: For equal roots of a quadratic equation, set \(D=0\) and remember to consider both positive and negative square roots.
Frequently asked questions
What is the correct answer to this question?
\(k=6\) or \(k=-6\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=k\), and \(c=9\), so \(D=k^2-36=0\). Thus, \(k^2=36\), giving \(k=6\) or \(k=-6\). Therefore, option A is correct. Exam tip: For equal roots of a quadratic equation, set \(D=0\) and remember to consider both positive and negative square roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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