Question

Find all real and imaginary solutions to the equation: X³ - 5x² + 4x - 20 = 0.

a) x = 2, x = 3, x = 4
b) x = -2, x = 2i, x = -2i
c) x = 5, x = -1, x = -4
d) x = 0, x = -5, x = 4

Answer 1

To solve the equation x³ - 5x² + 4x - 20 = 0, we use factoring and the quadratic formula. The real solutions are x = 2 and x = -5, and the complex solutions are x = 2i and x = -2i. Correct option is b)

Step-by-step explanation:

To solve the equation x³ - 5x² + 4x - 20 = 0, we can use a combination of factoring and the quadratic formula. First, we rearrange the equation to factor out a common factor: (x - 2)(x - 2)(x + 5) = 0. This gives us the real solution x = 2 and x = -5. Next, we can use the quadratic formula to find the complex solutions. The discriminant (√(b² - 4ac)) is negative, indicating that the solutions are imaginary. Plugging the values into the quadratic formula gives us x = 2i and x = -2i. Therefore, the correct answer is b) x = -2, x = 2i, x = -2i.