Kathy P. answered • 01/03/21

Mechanical Engineer with 10+ years of teaching and tutoring experience

Imaginary roots occur in conjugate pairs.

So, -9i is another root.

Therefore:

y = a(x - 4)(x - 9i)(x - (-9i))

y = a(x - 4)(x - 9i)(x + 9i)

Pick a = 1

y = (x - 4)(x - 9i)(x + 9i)

Recall: Difference of two squares.

a^2 - b^2 = (a - b)( a + b)

Therefore:

y = (x - 4)*[ x^2 - (9i)^2 ]

y = (x - 4)*[ x^2 - 81(-1) ]

y = (x - 4)(x^2 + 81)

Expand:

y = x^3 + 81x - 4x^2 - 324

y = x^3 - 4x^2 + 81x - 324

Stanton D.

You'll want to put that in an equation form: x^3-4x^2+81x-324 = 0 . Actually, you could have multiple roots in either of the two generating terms, i.e. use them as factors more than once. What do you think that might do to the graph of the function? You should definitely check!01/03/21