for which real values of c does the equation x^2 - 6x +c = 0 allow real solutions?

Question

1) For c ≤ 9

2) For c ≥ 6

3) For no real value of c

4) For c ≤ 4

5) For any real value of c

Answer 1

Ax² + Bx + C = 0 has real solutions as long as B² - 4AC ≥ 0.

So, 36 - 4(1)c ≥ 0

-4c ≥ -36

c ≤ 9