A third degree polynomial has the following three unique solutions: 2, 3 – 2i and k.

Question

a. What is the value of k?

b. What are the x & y intercepts of this polynomial?

Answer 1

When 3 - 2i is a solution, then the conjugate will automatically be a solution as well. The conjugate is 3 + 2i. So k = 3 + 2i.

The x-intercept will be "2" (that's what the solution means).

The y-intercept is not possible to determine. One possibility for the y-intercept can be found by multiplying out the following:

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

y = (x - 2)(x² - 6x + 13)

y = x³ - 8x² + 25x - 26

which makes this possibility have a y-intercept of -26. However, you can have the same solutions and have a multiplier in front of the function like this:

y = 2(x - 2)(x -(3 - 2i))(x - (3 + 2i)) which means the y-intercept would be -52

Or you could have this:

y = -3(x - 2)(x -(3 - 2i))(x - (3 + 2i)) which means the y-intercept could be 78.