Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 5, -3, and -1 + 3i

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.  5, -3, and -1 + 3i

anonymous · Answer

f(x) = x4 + 12.5x2 - 50x - 150
	f(x) = x4 - 9x2 - 50x - 150
	f(x) = x4 - 4x3 + 15x2 + 25x + 150
	f(x) = x4 - 4x3 - 15x2 - 25x - 150

anonymous · Answer

I got C but not sure if im correct!

campbell_st · Answer

well look at the complex root

x = -1 + 3i

then 

x + 1 = 3i

square both sides 

$$(x + 1)^2 = -9$$

so 

$$x^2 + 2x + 10 = 0$$

which means a quadratic factor is 

$$x^2 + 2x + 10$$

you know the real roots

x = 5    so   (x - 5) is a factor

x = -3  so  (x + 3) is a factor

then the polynomial is

$$P(x) = (x^2 + 2x + 10)(x -5)(x + 3)$$

so distribute to get the answer

and I don't think it's C

anonymous · Answer

f(x) = x4 - 9x2 - 50x - 150?

campbell_st · Answer

that's what I got...

anonymous · Answer

After I distributed thats what i got!

anonymous · Answer

oh okay :) thanks @campbell_st

campbell_st · Answer

since we agreee it looks like A might be the answer

anonymous · Answer

yes :) @campbell_st

campbell_st · Answer

great, well done