Question #N226
For what value of \(k\) does the equation \(x^2+6x+k=0\) have exactly one solution?
A. 9
B. 6
C. 3
D. 0
Correct Answer is: A
A quadratic equation has exactly one solution if and only if its discriminant is equal to 0. The discriminant of the quadratic equation \(ax^2 + bx + c = 0\) is \(b^2 - 4ac\). In this case, the discriminant is \(6^2 - 4 \cdot 1 \cdot k = 36 - 4k\). Setting the discriminant equal to 0 gives \(36 - 4k = 0\). Solving for \(k\) gives \(k = 9\).