Question

Write the equation in intercept form of the polynomial function with a single root of x = 2, double root of x = -2, has a root at x = 3i, and passes through the point .

Answer 1

The equation in intercept form is x^3 - 6x^2 + 8x + 12i = 0.

Step-by-step explanation:

To write the equation in intercept form, we need to find the x-intercepts of the function. Since the function has a single root at x = 2, a double root at x = -2, and a root at x = 3i, we can write the equation as:

(x - 2)(x + 2)(x - 3i) = 0

Expanding this equation, we get:

x^3 - 6x^2 + 8x + 12i = 0

Since the function passes through the point (2, 0), we can substitute x = 2 and solve for the constant:

(2)^3 - 6(2)^2 + 8(2) + 12i = 0

8 - 24 + 16 + 12i = 0

-16 + 12i = 0

Therefore, the equation in intercept form is:

x^3 - 6x^2 + 8x + 12i = 0