Question

find a cubic polynomial in standard form with real coefficients, having the given zeros.
0 and 2+3i

Answer 1

If 2 + 3i is a zero, then 2 - 3i is also a zero

x(x - 2 - 3i)(x - 2 + 3i)
= x(x² - 2x  + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i²
= x(x² - 4x + 4 + 9)
= x(x² - 4x + 13)
= x³ - 4x² + 13x