How do I write a quadratic equation whose solutions are 3+7i and 3-7i

Question

Math teacher didn't cover this at all in class and I have it as a homework problem. Thanks

Answer 1

IN GENERAL, the quadratic is (x-root#1)(x-root#2) = 0

so in your case you must multiply out (x-3-7i) times (x-3+7i), CAREFULLY, and you will get a quadratic with a, b & c all Reals.  To check the problem, calculate the discriminant, which should be -49.

Answer 2

f(x) = (x - (3 + 7i))(x - (3 - 7i))  relation between roots and factors

f(x) = (x - 3 - 7i)(x - 3 + 7i)

 

Can you multiply?