Find the largest value of k that makes the roots real (not imaginary). x^2+8x+k=0

Question

turingtest · Answer

so to keep our roots real we need to make sure the discriminant (the part under the radical in the quadratic formula) is at least 0 or greater$$8^2-4k \ge0 \rightarrow k \le16$$

anonymous · Answer

okay, i did that but i got $$k \le 16$$ how do i find out the biggest number? doesnt it have to be bigger than zero?

anonymous · Answer

$$ K \le 16 $$ means that the K cannot be greater than 16,so that is the maximum value of K for this problem.

anonymous · Answer

ohh okay and if im trying to make the roots imaginary, is the equation set less than 0?

turingtest · Answer

yep, and if the discriminant is set equal to zero you get a double root, i.e.
(x-2)(x-2)=0

anonymous · Answer

We have already assumed that in the discriminant part,so don't worry about that...

anonymous · Answer

okay, thanks!