Question

Determine the values of k so that the equation has two real roots.

x^2+8x+k=0​

Answer 1

k must be less than 16.

Explanation:

For the equation to have 2 distinct real roots the discriminant (b^2 - 4ac) must be greater than 0 zero.

So we have the inequality 8^2 - 4*1*k > 0.

Note if k is equal to 16 it will have duplicate roots ( both equal to 4).

4k < 64

k < 16 (answer).