If the two roots of the equation \(x^2+kx+9=0\) are equal, what is the correct condition for \(k\)?

Correct answer: \(k^2=36\)

For a quadratic equation \(ax^2+bx+c=0\), equal roots require the discriminant \(D=b^2-4ac\) to be zero. Here, \(a=1\), \(b=k\), and \(c=9\), so \(D=k^2-4(1)(9)=k^2-36\). Therefore, \(k^2-36=0\), giving \(k^2=36\). The other options result from using an incorrect value for \(4ac\) or from ignoring the discriminant condition. Exam tip: for equal roots, immediately set \(D=0\).