Final answer:
To find the coordinates of the points of intersection between the functions y = x² - 5x/x³ and y = 2x, set the two functions equal to each other and solve for x. The resulting equation is a cubic equation, which can be solved using factoring, the Rational Root Theorem, or a graphing calculator.
Step-by-step explanation:
To find the coordinates of the points of intersection between the functions y = x² - 5x/x³ and y = 2x, we need to set the two functions equal to each other and solve for x. So, we have:
x² - 5x/x³ = 2x
Multiplying both sides of the equation by x³ to get rid of the denominator, we have:
x² - 5x = 2x * x³
Simplifying further, we have a cubic equation:
x² - 5x = 2x⁴
To solve this cubic equation, we can rearrange it to bring all terms to one side of the equation and use factoring, the Rational Root Theorem, or a graphing calculator to determine the solutions.