Question

If a polynomial function f(x) has roots -9 and 7-i, what must be a factor of f(x)?

○ (x-(7 + 1))
O (x-(-7-1))
○ (x + (7 + 1))
O (x + (7-1)

Answer 1

(a) (x -(7 +i))

Explanation:

You want to know what must be a factor of f(x) if it has roots -9 and 7-i.

Complex roots

The complex roots of a polynomial with real coefficients are always found in conjugate pairs. Since 7-i is a root, its conjugate, 7+i, must also be a root. The corresponding factor is ...

(x -(7 +i))

If 7-i is a root of f(x), then (x -(7+i)) must be a factor.