Asked by Miki
Write an equation of lowest degree with real coefficients with the given zeros
root2, 3i
Please help! I don't understand this at all..
root2, 3i
Please help! I don't understand this at all..
Answers
Answered by
oobleck
if the coefficients are real, then complex roots come in conjugate pairs. So, if 3i is a root, so is -3i
So the polynomial is (x-√2)(x-3i)(x+3i) = (x-√2)(x^2+9)
If the coefficients are rational, then surds also come in conjugate pairs, so if √2 is a root, so is -√2
That means our polynomial is
(x-√2)(x+√2)(x-3i)(x+3i) = (x^2-2)(x^2+9)
So the polynomial is (x-√2)(x-3i)(x+3i) = (x-√2)(x^2+9)
If the coefficients are rational, then surds also come in conjugate pairs, so if √2 is a root, so is -√2
That means our polynomial is
(x-√2)(x+√2)(x-3i)(x+3i) = (x^2-2)(x^2+9)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.