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

A) f(x) = x^4 + 12.5x^2 - 50x - 150

B) f(x) = x^4 - 4x^3 + 15x^2 + 25x + 150

C) f(x) = x^4 - 4x^3 - 15x^2 - 25x - 150

D) f(x) = x^4 - 9x^2 - 50x - 150

Answer 1

I need help fast!

Answer 2

Because the polynomial has real coefficients and -1+3i is a zero of it, then -1-3i is a zero to it also !
So your polynomial is :
\[\Large f(x)=(x-5)(x+3)(x-(-1+3i))(x-(-1-3i))\]

Answer 3

Okay, how do I convert that to standard form?

Answer 4

We have :
\[\Large (x-5)(x+3)=x^2+3x-5x-15=x^2-2x-15\]
and :
\[\Large (x+1+3i)(x+1-3i)\\\Large=x^2+(1+3i)x+(1-3i)x+(1+3i)(1-3i)
\\\Large=x^2+2x+4
\]
So :
\[\Large f(x)=(x^2-2x-15)(x^2+2x+4)\]

Answer 5

5, -3, and -1 + 3i

remamber that those have a conjugate pair. THe imaginaries

(x-5)*(x+3)*(x-(-1 + 3i ))*(x+(-1 + 3i )) now expand

Answer 6

OK ! It was there a mistype :
\[\Large (x+1+3i)(x+1−3i)=x^2+2x+10\]

Answer 7

x^4-2 x^3-(7-6 i) x^2-(16+12 i) x-(120+90 i)

Answer 8

i'd go with noura