Form a polynomial f(x) with real coefficients having the given degree and zeros

Question

degree 4; zeros : -3 + 3 i ; 4 multiplicity 2

enter the polynomial

f(x) = a ( )

Answer 1

Form a polynomial f(x) with real coefficients having the given degree and zeros

degree 4; zeros : -3 + 3 i ; 4 multiplicity 2

=>

f(x) = (x - (-3+3i) )(x -(-3-3i) ) (x-4)(x-4)

= ((x-(-3)+3i )(x-(-3) - 3i)(x² - 8x +16)

= ((x+3) +3i)((x+3) -3i )(x² -8x+16)

= ((x+3)² -(3i)² )(x² -8x +16)

=((x² +6x+9)-(9i² ))(x² -8x +16)

=(x² +6x+9 -(9(-1))(x² -8x +16)

=(x² +6x+9 +9)(x² -8x +16)

=(x² +6x+18)((x² -8x +16))

=x²(x² -8x +16) +6x(x² -8x +16)+18(x² -8x +16)

=x⁴ -8x³+16x² +6x³ -48x² +96x +18x² -144x +288

=x⁴ - 2x³ 14x² -48x +288