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

Sagot :

KimSiJeong

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

Corsaquix

Answer:

[tex](x-(7-i))[/tex]

Step-by-step explanation:

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

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

[tex](x-(-9)\implies (x+9)\\(x-(7-i))\impli[/tex]

Therefore, the desired answer is [tex]\boxed{(x-(7-i))}[/tex]

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