SOLUTION: Hello! Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 1 + i and 1

SOLUTION: Hello! Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 1 + i and 1 - i. thanks

Question 199782: Hello!
Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions.
P has degree 2, and zeros 1 + i and 1 - i.
thanks for the homework help!
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If and are roots of the equation , then and are factors of the trinomial .

So the product of:

will result in the desired monic univariate polynomial.

Hints:

1. Treat and as single numbers and apply FOIL.

2. results in the difference of two squares.

3. Remember that

John

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
or Start with the given zeros

or Get the constants to the left side

or Square both sides

or Square i and -i to get -1

Since the equations are the same, we can focus on the first equation

FOIL

Add 1 to both sides.

Combine like terms.

So the polynomial has zeros of 1+i and 1-i

-------------------------------

Check:

You can check the answer with the quadratic formula.

Notice that the quadratic is in the form of where , , and

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Break up the fraction for each case.

or Reduce.

So the zeros are or which confirms our answer.
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