Question

For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?

Answer 1

K has no solutions.

Explanation:

Because the parabola opens upwards and the y-intercept is non-negative, the parabola cannot cross the x-axis twice. Duh.

Answer 2

for the graph to cross the x axis twice, b²-4ac needs to be larger than 0
b=-k, a=1, c=k²
b²-4ac=k²-4k²=-3k²
-3k² will never be larger than 0.