Given the xeros 0, 2, 1 + i, 1 - i, write the polynomial
I have no idea
When you solved polynomials (starting with solving quadratic equations), you factored, set the factors equal to zero, and solved the resulting linear equations. When you couldn't factor the quadratic down to linear factors (like "3x + 4"), you solved the quadratic factor by applying the Quadratic Formula.Given the xeros 0, 2, 1 + i, 1 - i, write the polynomial
By working backwards from the zero, and by using parentheses to make my meaning clear (to myself).how did you get x - 1 - i?
Yes!so the other zero is x = 1 - i, so x - (1 - i) = x - 1 + i?
I'd work vertically, and probably keep the parentheses:how do you multiply it?
vertical set-up: x - (1 + i) x - (1 - i) ------------------------------- - (1 - i)x + (1 + i)(1 - i) x^2 - (1 + i)x -------------------------------Multiplying the conjugates is easy: that's just the reverse of factoring a difference of squares. The rest simplifies nicely, and you can add down to get the quadratic below the second "equals" bar.