Question

write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4i and square root of 3

Answer 1

the other two zeros must be
\[-4i,-\sqrt3\] multiply
\[(x-4i)(x+4i)(x-\sqrt3)(x+\sqrt3)\]

Answer 2

not nearly as hard as it looks
\[(x+4i)(x-4i)=x^2+16\] and
\[(x-\sqrt3)(x+\sqrt3)=x^2-3\]

Answer 3

your real job then is only to multiply
\[(x^2+16)(x^2-3)\]

Answer 4

So, it would end up being x^4 + 13x^2 - 48

Answer 5

thank you! @satellite73

Answer 6

yw