Question

Determine all values of k for which the roots of the equation x^2-6x+k=0 are imaginary

Answer 1

Use the discriminant in the quadratic formula.
When the discriminant is less then zero, the roots are imaginary.

b^2 - 4ac < 0

(-6)^2 - 4(1)(k) < 0

36 -4k < 0

-4k < -36

k > 9