Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.
3, 4+i
+128474 If 4 + i is a root, so is 4-i
The polynomial will be of degree 3 and will be of the form ax^3 +bx^2 + cx + d
a = 1
b = the sum of the roots = - ( 3 + 4+i + 4 - i) = -11
c = (3(4+i) + 3(4 -i) + (4 + i) (4 - i) ) = ( 12 + 3i + 12 - 3i + 16 - i^2) = (40 - - 1) = 41
d = - [ (3) (4 + i) ( 4- i) ] = - [ 3 ( 16 - i^2)] = - [3 * 17] = -51
So....the polynomial is
x^3 - 11x^2 + 41x - 51
