Find the largest integral value of k so that the rots of x^2+6x+k+0 are real.

Answer 1

For the roots to be real, the part under the radical in the quadratic formula -- b squared minus 4 times a times c -- must not be negative. Here b=6, a=1 and c=k. So:

36 - 4k ≥ 0

36 ≥ 4k

9 ≥ k

So the largest possible value of k for which the roots will be real is 9.