Write the equation of a polynomial that has 2 and 3-i as roots

Step-by-step explanation:

complex roots always occur in pairs.

roots are 2,3i,-3i

f (x) = (x-2) (x-3i) (x+3i)

= (x-2) (x² - (3i) ²)

= (x-2) (x²-9i²)

= (x-2) (x²+9)

=x³-2x²+9x-18

if the roots are 2±3i or 2+3i and 2-3i

f (x) = (x - (2+3i)) (x - (2-3i))

=[ (x-2) - 3i][ (x-2) + 3i]

=[ (x-2) ² - (3i) ²]

=x²-4x+4-9i²

=x²-4x+4+9

=x²-4x+13