Question

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

Answer 1

Answer:

$(x-(7-i))$

Step-by-step explanation:

For a polynomial with roots $a$ and $b$, the polynomial $f(x)$ can be written in factored form $(x-a)(x-b)$. That way, when you plug in any of the roots, $f(x)$ returns zero.

Since the polynomial has at least two roots-9 and 7-i, two of its factors must then be:

$(x-(-9)\implies (x+9)\\(x-(7-i))\impli$

Therefore, the desired answer is $\boxed{(x-(7-i))}$

Answer 2

Answer:

f(x) = [x-(7-2i)][x-(7+2i)]

= [(x-7)+2i][(x-7)-2i]

= (x-7)2 - (2i)2

= x2 - 14x + 49 - 4i2 = x2 - 14x + 49 +4

= x2 - 14x + 53