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elizabeth

12-28-2013, 04:38 PM

Complex zeroes Subject test Math level 2

Which of the following is a factor of P(x) given that 1+i is a zero of this polynomial?

(A) 1+i

(B) 1-i

(C) x-(1+i)

(D) x-(1-i)

(E) -1-i

Thanks!

Oliver

12-28-2013, 04:39 PM

Complex roots occur in conjugate pairs which means that if a polynomial with real coefficients has a root of the form a+bi then a-bi is also a root.

Based on the aforementioned theorem we have that the other root is equal to 1-i .

So, the factor that corresponds to this root is x-(1-i)

Therefore the correct answer is (D).

elizabeth

12-28-2013, 04:40 PM

Complex roots occur in conjugate pairs which means that if a polynomial with real coefficients has a root of the form a+bi then a-bi is also a root.

Based on the aforementioned theorem we have that the other root is equal to 1-i .

So, the factor that corresponds to this root is x-(1-i)

Therefore the correct answer is (D).

thanks!!:)

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