Answer:
D) c < 9
Step-by-step explanation:
To find the values of c that will result in the equation having exactly two distinct real solutions, we need to use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a.
In this case, our equation is X²+6x+c=0, which can be rewritten as x² + 6x + c = 0. Comparing this to the general form of a quadratic equation ax² + bx + c = 0, we have a = 1, b = 6, and c = c.
For the equation to have two distinct real solutions, the discriminant (b^2 - 4ac) must be positive. So, we have:
b^2 - 4ac > 0
6^2 - 4(1)(c) > 0
36 - 4c > 0
36 > 4c
9 > c
Therefore, the correct statement is D) c < 9.
