Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. (5 points) 4, -8, and 2 + 3i

Answer 1

We need a matching complex to 2+3i. The conjugate is 2-3i and the two factors are (x-2-3i)(x-2+3i)=(x²-4x+4+9)=x²-4x+13.
The polynomial is (x-4)(x+8)(x²-4x+13)=(x²+4x-32)(x²-4x+13)=
x⁴-4x³+13x²
+4x³-16x²+ 52x
-32x²+128x-416
x⁴-35x²+180x-416 is the 4th degree polynomial.