SOLUTION: Verify that P(x) = x^3 - x^2 - ix^2 - 20x + ix + 20i has a zero of i and that its conjugate -i is not a zero. Explain why this does not contradict the Conjugate Pair Theorem.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Verify that P(x) = x^3 - x^2 - ix^2 - 20x + ix + 20i has a zero of i and that its conjugate -i is not a zero. Explain why this does not contradict the Conjugate Pair Theorem.      Log On


   

Question 57257This question is from textbook Applied College Algebra
: Verify that P(x) = x^3 - x^2 - ix^2 - 20x + ix + 20i has a zero of i and that its conjugate -i is not a zero. Explain why this does not contradict the Conjugate Pair Theorem. This question is from textbook Applied College Algebra

Answer by Scriptor(36) About Me  (Show Source):
You can put this solution on YOUR website!
Just fill in i in your function and check if it becomes 0.
Make use of the property that i² = -1
P(i) = i³ - i² -i*(i²) -20i + i*i + 20i
= -i + 1 + i - 20i - 1 + 20i
= 0
Check for yourself that P(-i) is NOT equal to zero (same mehod as above)
This does not contradict the Conjugate Pair Theorem, because not all the coefficients of P(x) are real.
Greets,
Scriptor