Final answer:
To solve the equation f(x) = 2x³ - 3x² - 12x + 1, we can factor or use the quadratic formula. Factoring gives us two possible solutions: x = 1 or 2x² + x - 1 = 0. Using the quadratic formula, we find x = 1 and x = -1.
Step-by-step explanation:
To solve the equation f(x) = 2x³ - 3x² - 12x + 1, we need to find the values of x that make the equation true. We can do this by factoring the equation or using the quadratic formula.
Factoring the equation, we can rewrite it as (x-1)(2x² + x - 1) = 0. Setting each factor equal to 0, we find two possible solutions: x = 1 or 2x² + x - 1 = 0.
Using the quadratic formula, we can solve the equation 2x² + x - 1 = 0 to find the values of x. The quadratic formula is x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values a = 2, b = 1, and c = -1, we get x = (-1 ± sqrt(1 + 8)) / 4. Simplifying further, we have x = (-1 ± sqrt(9)) / 4. This gives us two possible solutions: x = (-1 + 3) / 4 = 1 and x = (-1 - 3) / 4 = -1.
Learn more about Solving Polynomial Equations