Question

Writing Polynomial Functions from Complex Roots

Pre-Test
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If a polynomial function f(x) has roots -9 and 7-i, what must be a factor of f(x)?
O (x-(7 + 1))
O (x-(-7-1))
O (x + (7 + 1))
O (x + (7-1))

Answer 1

If a polynomial function has roots -9 and 7-i, the factors of the function will be (x+9)(x-7+i)(x-7-i).

Step-by-step explanation:

If a polynomial function f(x) has roots -9 and 7-i, then the factors of f(x) can be found by using the complex conjugates of the given roots. The complex conjugate of 7-i is 7+i. So, the factors of f(x) will be (x-(-9))(x-(7-i))(x-(7+i)). Simplifying this expression, we get (x+9)(x-7+i)(x-7-i).

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