## babydoll332 2 years ago Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -2, and -1 + 2i

1. babydoll332

f(x) = x4 - 3x3 + 8x2 + 13x + 40 correct

2. satellite73

start with \[(x-4)(x+2)(x-(-1+2i))(x-(1-2i))\] and multiply out but before we being the last product is very easy

3. babydoll332

can you kinda go back words with me work best that way please and thanks

4. satellite73

if the zeros are \(a+bi\) and \(a-bi\) the quadratic is \[x^2-2ax+(a^2+b^2)\] in your case it is \[x^2+2x+5\]

5. satellite73

ok lets start at the very beginning

6. satellite73

if \(-1+2i\) is a zero, then so is its conjugate \(-1-2i\)

7. satellite73

the quadratic equation that will have those two zeros is \[x^2+2x+5\] is it clear how i got that?

8. babydoll332

rightt i got that

9. satellite73

oh ok good then your final job is to multiply out \[(x-4)(x+2)(x^2+2x+5)\]

10. babydoll332

f(x) = x4 - 7x2 - 26x - 40

11. satellite73

you can do it in any order you like , but as you can see it is a bunch of algebra you have to do. yes, that is correct

12. babydoll332

thankkkksss

13. satellite73

yw, it looks like you did it on your own good job