How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3i, -3i, 5?

Question

1749 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-03T07:00:12

#y = (x -5)(x - 3i)(x - -3i) = x³ - 5x² + 9x - 45#

With any polynomial the with roots #r_1, r_2, r_3, ... r_n#, the factors are:

#y = k(x - r_1)(x - r_2)(x - r_3)...(x - r_n)#

In this case, we are given that k = 1, and the roots are #5, 3i, and -3i#. This makes the factors:

#y = (x -5)(x - 3i)(x - -3i)#

I will multiply the factors one-pair-at-a-time:

#y = (x - 5)(x² + 9)#

#y = x³ - 5x² + 9x + 45#