Write a polynomial function of least degree with integral coefficients that has the given zeros. 0, 5, 3 + i need to show all work
Mathematics
everkayy
Question
Write a polynomial function of least degree with integral coefficients that has the given zeros.
0, 5, 3 + i
need to show all work
0, 5, 3 + i
need to show all work
1 Answer

1. User Answers MissPhiladelphia
The zeroes are
0, 5, 3 + i (and its conjugate)
The factors are
x (x + 5) (x  (3 + i)) (x  (3  i))
Expanding...
(x² + 5x)((x  3)  i) ((x  3) + i)
(x² + 5x)((x  3)²  i²)
(x² + 5x)(x²  6x + 9  (1))
(x² + 5x)(x²  6x + 10)
x⁴  6x³ + 10x² + 5x³  30x² + 50x
x⁴  x³  20x² + 50x