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)
Write an equation of lowest degree with real coefficients with the given zeros
root2, 3i
Please help! I don't understand this at all..
1 answer