Hello, Instigator!

Here's #2 . . .

2) Find a fourth-degree polynomial with the rational coefficients

. . where and are two of the four zeros.

You're expected to know these facts . . .

If is a zero, then its conjugate, , is also a zero.

If is a zero, then its conjugate, , is also a zero.

The polynomial is: .

Multiply and simplify: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

If the thought of that multiplication fills you with Fear and Loathing,

. . let me show you a trick for handling "conjugate multiplication".

The first product is: .

. . Regroup it like this: . . . . This is:

. . So we have: .

The second product is: .

. . Regroup it like this: . . . . This is:

. . So we have: .

Then we can multiply: . . . . see?