Asked by Rose

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 :)

Answers

Answered by Damon
You only typed half the problem. Perhaps you are supposed to graph, not solve?
Answered by Rose
sorry, i forgot to say the instructions said "find all possible rational roots"
Answered by Damon
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
Answered by Damon
That is from:

http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php
Answered by Damon
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
Answered by Damon
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.
Answered by Damon
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.
Answered by Rose
thank you so much for your help ! :)

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