If \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.

Answer Details

If the equation \(x^{2} - kx + 9 = 0\) has equal roots, it means that the discriminant is zero. The discriminant is the expression inside the square root in the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a For the equation \(x^{2} - kx + 9 = 0\), the discriminant is: b^2 - 4ac = k^2 - 4(1)(9) = k^2 - 36 Since the roots are equal, the discriminant is zero: k^2 - 36 = 0 k^2 = 36 k = ±6 Therefore, the values of k that make the equation have equal roots are \(\pm6\).