write a polynomial function of least degree with integral co

write a polynomial function of least degree with integral coefficients that have the given zeros, 0, -5, 3+i

Solution

Dear Student

Thank you for using Chegg !!

Given a polynomial with zeroes 0, -5, 3 + i . Now if 3+i is a zero of the polynomial implies 3 - i must also be a zeo since complex roots occur in pairs.

Hence the lest degree polynomial shall be of the form

(x) (x + 5) (x -3 -i) (x - 3 + i) = 0

(x)(x+5) (x^2 -6x + 10) = 0

(x)(x^3 - x^2 - 20x + 50 ) = 0

(x^4 - x^3 -20x^2 + 50x = 0

Solution