Final answer:
To find the intercepts over the complex plane for the given equation, we set y to 0 and solve for x. The equation has 2 intercepts over the complex plane.
Step-by-step explanation:
The equation is y = (4x^2 + 1)(x^2 - 8)x. To find the intercepts over the complex plane, we need to determine the values of x when y = 0. Setting y to 0 gives us (4x^2 + 1)(x^2 - 8)x = 0. We can find the intercepts by solving this equation.
Since the equation is a product of multiple terms, we can set each term equal to zero separately:
- 4x^2 + 1 = 0
- x^2 - 8 = 0
- x = 0
Solving each equation gives us the values of x where the equation equals zero. After solving, we find two intercepts over the complex plane, which means the answer is b. 2 intercepts.