Posted by **Rose** on Saturday, September 8, 2012 at 8:37pm.

Can someone show me the steps for how to solve:

1.) f(x) = 4x^4 -3x^3 +2x^2 +x-3

2.) f(x) = x^3 - 2x^2 -5x +6

3.) f(x) = -3x^3 -2x^2 + x -1

Thank you so much :)

- For what x ? -
**Damon**, Saturday, September 8, 2012 at 8:42pm
You only typed half the problem. Perhaps you are supposed to graph, not solve?

- Math -
**Rose**, Saturday, September 8, 2012 at 9:09pm
sorry, i forgot to say the instructions said "find all possible rational roots"

- Math -
**Damon**, Saturday, September 8, 2012 at 9:23pm
Result:

The roots of the polynomial 4x4 - 3x3 + 2x2 + x - 3 are:

X1 = 0.301 + 1.002*i

X2 = 0.301 - 1.002*i

X3 = 0.905

X4 = -0.757

- Math -
**Damon**, Saturday, September 8, 2012 at 9:24pm
That is from:

http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php

- Math -
**Damon**, Saturday, September 8, 2012 at 9:26pm
As you can see you really have to graph that polynomial to find the roots. If you have a graphing calculator, try that

Notice that it only crosses the x axis twice and then has a complex pair for the third and fourth roots

- Math -
**Damon**, Saturday, September 8, 2012 at 9:27pm
For the second one you can see that one is a root by inspection.

Then you can divide by (x-1) to get a quadratic which you can solve.

- Math -
**Damon**, Saturday, September 8, 2012 at 9:42pm
By the way if you tried all possible rational roots results on the first problem using factors of the first and last term 3 and 4 ( 3, 2, 4) you would have found that it has no rational factors by the rational root test.

- Math -
**Rose**, Sunday, September 9, 2012 at 12:12am
thank you so much for your help ! :)

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