SOLUTION: Find a quadratic equation with roots (4+i) and (4-i).

Question 166677: Find a quadratic equation with roots (4+i) and (4-i).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Since and are given zeros this means that:

and

Get all terms to the left side in each case

and

Now use the zero product property in reverse to join the factors.

Regroup the terms.

Now let . So the equation is now:

FOIL

Plug in and

Rewrite as

FOIL

Combine like terms.

-------------------------------------------
Answer:

So the polynomial with roots of and is

Note: you can verify the answer by use of the quadratic formula.
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