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

Question 176614: Find a quadratic equation with roots (4+i) and (4-i)
Found 3 solutions by solver91311, josmiceli, Earlsdon:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
If then is a factor of the quadratic. Similarly, is a factor of the quadratic and we can say:

.

Just multiply the two factors to get back to the original quadratic. Hints: Treat these two factors as binomials with being one term and as the other term. Remember that multiplying a conjugate pair results in the difference of two squares, that is: . Therefore
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
I can write

This equation is true if either
or
The function y(x) is

note that

check:

OK
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Find the quadratic equation whose roots are: and
Basically, we'll work in reverse of solving the quadratic equation, starting with:
and rewrite these as:
and ...and we know that these are factors of the original quadratic equation, so we can reconstitute the equation by multiplying these factors. First, simplify the factors.
Now we'll perform the multiplication.
Now we'll simplify this.

The original quadratic equation is:

Let's check using the quadratic formula:

or Simplifying, we get:
or

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