Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree​ 4; ​ zeros: 3−5i; −1 multiplicity 2

Answer 1

3 - 5i is a zero

imaginary zeros come in conjugate pairs so

3+ 5i is also a zero

x = 3- 5i

x-3 = -5i

x^2 -6x + 9 = -25

x^2-6x +34 = 0

x = -1

x+1 = 0 it's multiplicity 2 so

(x+1)(x+1) = 0

(x+1)^2 = 0

x^2 +2x + 1 = 0

two factors of the 4th degree polynomial are

(x^2-6x +34)(x^2+2x + 1)

= x^4 -4x^3 +23x^2 + 62x + 34 is the 4th degree polynomial