Final answer:
The equation f(x) = x³ - 2x² - 15x - 36 can be solved using various methods like factoring, synthetic division, or the rational root theorem. By using these methods, we can determine that the equation has three real solutions.
Step-by-step explanation:
This equation can be solved using the quadratic formula. For an equation of the form ax² + bx + c = 0, the discriminant (b² - 4ac) is used to determine the number of real and imaginary solutions. If the discriminant is positive, there are two distinct real solutions. If the discriminant is zero, there is one real solution (a double root). If the discriminant is negative, there are two complex (imaginary) solutions.
In the given equation, f(x) = x³ - 2x² - 15x - 36, we have a cubic equation. The discriminant is not directly applicable in this case. To find the solutions, we can use methods like factoring, synthetic division, or the rational root theorem. By using synthetic division or the rational root theorem, we can find that the equation has three real solutions. Therefore, Option 1: 3 real solutions, is the correct answer.