Question

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

7, -11, and 2 + 6i

f(x) = x4 - 53x2 + 468x - 3080

f(x) = x4 - 9x3 - 42x2 + 234x - 3080

f(x) = x4 - 117x2 + 468x - 3080

f(x) = x4 - 9x3 + 42x2 - 234x + 3080

Answer 1

\[the~ zeros~ are~ 7,-11,2+6 \iota,2-6 \iota\]
\[f \left( x \right)=\left( x-7 \right)\left( x+11 \right)\left\{ x-\left( 2+6 \iota \right) \right\}\left\{ x-\left( 2-6 \iota \right) \right\}\]
simplify and get the required polynomial.