hard precalculus problem. Determine k so that the equation x^2 -3x + K =0 has a double root?

Question

Determine k so that the equation x^2 -3x + K =0 has a double root

Answer 1

x^2 -3x + K =0
b^2-4ac > 0 for a double root to occur
so 9 -4K >0
9>4K
9/4 = 2.25 >K or, same thing, K <2.25

Answer 2

Since this is a 2nd order equation, and also a quadratic, it will be calculated that x will have two values (double root). However, to prevent it from being imaginary, √(9-4k) must be ≥ 0. That means that the value for 4k cannot be greater than 9. Therefore, K ≤ 9/4, or K ≤ 2.25.