How do you know that (k-2)² ≥ 0 ? that's the discriminant
thingy, i know. but what about the 8 that is inside the equation
you've written?
(any real equation/function/expression)² ≥ 0. e.g. (-1)² =
1, (-4)² = 16. dun ask why, at your stage, anything squared must be
positive, until you go JC where you deal with unreal/complex
numbers.
if (k-2)² ≥ 0, then (k-2)² + 8 ≥ 8, which is
definitely positive or > 0.
For your question, you are required to show the roots of an
equation are real. You will simply need to prove that its
root is always positive (and not zero and/or negative), thus
completing the square is the fastest way to achieve this.
