SOLUTION: "Find the roots of the polynomial equation." 2x^3+2x^2-19x+20 I tried factoring out a 2 but it is uneven. Can I still find the roots and solve the problem even when the x^3 coeffi

Question 696202: "Find the roots of the polynomial equation." 2x^3+2x^2-19x+20
I tried factoring out a 2 but it is uneven. Can I still find the roots and solve the problem even when the x^3 coefficient is two?
I need this right now ASAP because I have an Alg. 2 final tomorrow, thanks
Found 2 solutions by solver91311, KMST:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Start with the Rational Roots Theorem. If a polynomial equation with integer coefficients has a rational root, then that root must be of the form where is a factor of the constant term and is a factor of the lead coefficient.

Hence your possible rational zeros are:

Start testing the possible zeros one at a time using Synthetic Division. Review the process for Synthetic Division here (note: there are 4 pages to review).

Once you find one that works, you will have one of your binomial factors, and the quotient of the synthetic division will give you a quadratic trinomial that you can solve with the quadratic formula. Hint: start with -4.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The rational roots of (if they exist) will be of the form
and where is a factor of the independent term and is a factor of the leading coefficient .
Factors of : , , , , , . Factors of : , .
Possible rational roots: , , , , , , , , , , , , , , , and .
I tried them, and found that , and that

The roots would be ,
and the solutions to .
However, has no real solution.
If you are studying complex numbers, you could find another two complex roots.
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