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 :)
8 answers
You only typed half the problem. Perhaps you are supposed to graph, not solve?
sorry, i forgot to say the instructions said "find all possible rational roots"
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
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
That is from:
http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php
http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php
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
Notice that it only crosses the x axis twice and then has a complex pair for the third and fourth roots
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.
Then you can divide by (x-1) to get a quadratic which you can solve.
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.
thank you so much for your help ! :)
2 answers