Question

Write a polynomial functionſ of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 1,3, and

Answer 1

Answer:

f(x) = $x^{4} - 8x^{3} + 24x^{2} - 32x + 15$

Step-by-step explanation:

First of all, if 2 - i is a zero, then so is 2 + i

All you need to do now is multiply (x - 1)(x - 3)(x - 2 + i)(x - 2 - i)

I will do part of that multiplication

(x - 2 + i)(x - 2 - i) = $x^{2}$ - 2x - xi - 2x + 4 + 2i + xi - 2i - $i^{2}$

                           = $x^{2}$ - 4x + 5

So, now (x - 1)(x - 3)($x^{2}$ - 4x + 5) =  $x^{4} - 8x^{3} + 24x^{2} - 32x + 15$

I will let you finish that multiplication.  I did some and you can do some.  OK?