Question

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

Degree 4;
zeros: -4-5i; - 5
multiplicity 2

Let a represent the leading coefficient. The polynomial is f(x) = a(________)

(Type an expression using x as the variable. Use integers or fractions for any
numbers in the expression. Simplify your answer.)

Answer 1

Answer:
`x^4 +2x^3 -14x^2 +210x+1025`

Explanation:

By the conjugate root theorem, -4+5i is also a root.

`f(x)=a(x+4-5i)(x+4+5i)(x+5)^2\\\\=a(x^2 -8x+41)(x+5)^2\\\\ =a(x^2 -8x+41)(x^2 +10x+25)\\\\=a(x^4 +2x^3 -14x^2 +210x+1025)`