1. Let f(x)=3x²-kx+m where m and k are real numbers. Find the roots of f(x). What values of k and m does f(x) have complex roots?
2. Raul claims that the sum of the roots of a quadratic equation is always equal to -b/a. Is that correct?
1. use the quadratic formula as usual to find the roots. To have complex roots, you need a negative discriminant. That is,
k^2 - 12m < 0
There are infinitely many values of k and m that will satisfy this condition.
2. True. Look at the roots produced by the quadratic formula.