If the two roots of the equation \(x^2+kx+36=0\) are equal, what are the possible values of \(k\)?
Answer and explanation
Correct answer: \(k=12\) or \(k=-12\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here \(a=1\), \(b=k\), and \(c=36\), so \(D=k^2-4(1)(36)=k^2-144\). Therefore, \(k^2-144=0\), giving \(k^2=144\) and \(k=\pm12\). Exam tip: For equal roots of a quadratic equation, set the discriminant directly equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(k=12\) or \(k=-12\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here \(a=1\), \(b=k\), and \(c=36\), so \(D=k^2-4(1)(36)=k^2-144\). Therefore, \(k^2-144=0\), giving \(k^2=144\) and \(k=\pm12\). Exam tip: For equal roots of a quadratic equation, set the discriminant directly equal to zero.
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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