SOLUTION: find all the roots of f(x) = x^4-4x^3+6x^2-4x+5 if 2-i is one root

Question 637985: find all the roots of f(x) = x^4-4x^3+6x^2-4x+5 if 2-i is one root
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If

is a zero, then

is also a zero because complex zeros of polynomial functions always come in conjugate pairs.

If

is a zero of a polynomial function, then

is a factor of the polynomial.

So now you have two factors of the original polynomial:

Multiply them using FOIL (treating the complex quantities as single values -- remember that the product of a pair of conjugates is the difference of two squares and that

The result will be a quadratic trinomial. Use this as the divisor of the original 4th degree polynomial using polynomial long division. Click the link: Purple Math Polynomial Long Division if you need a refresher on this process.

The quotient of the long division process will be a quadratic polynomial that is the product of the two remaining factors of the original polynomial. Use thee quadratic formula to determine the two remaining zeros.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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