Question

Find the intercepts over the complex plane for the equation y = (4x^2 + 1)(x^2 - 8)x.

a. 0 intercepts
b. 2 intercepts
c. 4 intercepts
d. 6 intercepts

Answer 1

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:

1. 4x^2 + 1 = 0
2. x^2 - 8 = 0
3. 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.