Question

How do write a function whose coefficient of the highest degree term is 2, and which has zeroes of 1, 4, 2i and -2i?

Answer 1

Since you know values of when the function is zero, you can make a polynomial out of individual factors (x - 1), (x - 2i), etc. All you need to do then is simplify it and manipulate it to make the highest degree term have a coefficient of 2.

Answer 2

If the coefficient of the highest degree term is 1, it is easy. Would be (x-1)(x-4)(x-2i)(x+2i). However, increasing the coefficient of the highest degree term to 2 stumps me.

Answer 3

From the factors (x - 1)(x - 4)(x - 2i)(x + 2i), you know that your highest degree term will be x^4 with a coefficient of 1. All you need to do is multiply through by 2; this doesn't affect the zeroes of the function!

Answer 4

When you say multiply through by 2, do you mean change each x to 2x?

Answer 5

No, you just put 2 in as one of the factors: 2(x - 1)(x - 4)(x - 2i)(x + 2i).

Answer 6

Much thanks!

Answer 7

You're welcom.e :)