|
Question 134744This question is from textbook Algebra and trigonomerty
: Suppose the polynomial function has the given zero.
Find the other zeros.
f(x)= x^3 - x^2 + x -1; 1
This question is from textbook Algebra and trigonomerty
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! Suppose the polynomial function has the given zero.
Find the other zeros.
f(x)= x^3 - x^2 + x -1; 1
Since f(x) is a degree 3 polynomial we know that there are 2 other possible solutions. We can use synthetic division to find the reduced form of f(x), which will be a quadratic equation which we can solve from there.
Synthetic division is done by writing the thing you are dividing by on the left hand side of a bar and then all the leading coeficciants of f(x) across a row on the right hand side of the bar. Then skip a line and bring down the first leading coeifficent. Multiply that by the thing your dividing by and write that under the second number in the row on the right hand side. Add those two numbers and then multiply that sum by the thing your dividing by and write that under the third number in the row. Repeate this until all of your second row is filled in. It should look something like this:
1| 1 -1 1 -1
| 1 0 1
------------------------------
1 0 1 0
so we know that f(x) factors down to (x-1)(x^2+1). Now x^2+1 has no real solutions but it has two imaginary solutions of +i and -i. So if you are asked for just the real solutions the only one is 1 but if your looking for all the solutions(real and imaginary) then they are 1,i,and -i.
|
|
|
| |
