Question

Spud has a problem. He knows that the roots of a quadratic function are x=3+4i and x=3−4i, but in order to get credit for the problem he was supposed to have written down the original equation. Unfortunately, he lost the paper with the original equation on it. Luckily, his friends are full of advice.

B:Hugo says, “No, no, no. You can do it that way, but that’s too complicated. I think you just start with x=3+4i and work backwards. So x–3=4i, then, hmmm… Yeah, that’ll work.” Try Hugo’s method.​

Answer 1

x² -6x +22 = 0

Explanation:

You want to write the quadratic equation that has roots x = 3±4i, starting from x -3 = ±4i.

Quadratic

The next step would be to square both sides of the equation:

(x -3)² = (±4i)²

(x -3)² = 16i² = -16

(x -3)² +16 = 0 . . . . . . add 16

x² -6x +22 = 0 . . . . . expand the square