Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

2, -4, and 1 + 3i
I know the polynomial is (x-2)(x + 4)(x - (1+3i)
but do I do next?

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 

2, -4, and 1 + 3i
I know the polynomial is (x-2)(x + 4)(x - (1+3i) 
but do I do next?

thomas5267 · Answer

Note that is not the whole list of zeros.  This is because for a real coefficient polynomial, complex roots must come in conjugates.

chris215 · Answer

ok but im not sure what to do next

welshfella · Answer

do you know what the conjugate of 1 + 3i is?

chris215 · Answer

no

welshfella · Answer

just replace the + by -

welshfella · Answer

1 - 3i

chris215 · Answer

ok so I got f(x) = x^4 - 3x^3 + 6x^2 - 18x + 80

thomas5267 · Answer

I don't think the answer is correct.  Try again and remember that $(1-3i)(1+3i)=1^2-(3i)^2=1-(-9)=10$.

welshfella · Answer

( x  - (1+ 3i) (x - (1-3i) = x^2 -x(1 + 3i) - x(1 - 3i0  + (1+31)(1-31)
   =    x^2 - 2x + 10