101k views
4 votes
Which one of the following is a polynomial with real coefficients that has 2 and. 2-i as zeroes

User JoaMika
by
8.4k points

1 Answer

3 votes

Final answer:

The polynomial with real coefficients that has 2 and 2-i as zeroes is x^3 - 6x^2 + 13x - 10.

Step-by-step explanation:

The polynomial with real coefficients that has 2 and 2-i as zeroes can be found by using the fact that complex zeroes come in conjugate pairs. Given that 2-i is a zero, its conjugate 2+i must also be a zero. We can then find the polynomial by multiplying the factors (x-2)(x-(2+i))(x-(2-i)).

Expanding this expression, we get (x-2)(x-2-i)(x-2+i) = (x-2)(x^2-4x+5).

Therefore, the polynomial with real coefficients is x^3 - 6x^2 + 13x - 10

User Slkorolev
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories