How do you use the rational root theorem to find the roots of #5x^4 + 9x^3 + 5x^2 + 2x + 4 = 0#?
2 Answers
List the possible rational roots and then test them. None of them are roots.
Explanation:
For
The divisors of
The divisors of
So,the possible rational roots are:
Since all of the coefficients are positive, there can be no positive roots.
Testing by synthetic division we can find that
So we need to test
The equation has no rational roots.
Any rational roots must be
None of these are roots, so it has no rational roots.
Explanation:
Let
By the rational root theorem, the rational roots of
So the only possible rational roots are
None of these are roots, so there are no rational roots.
In fact
graph{5x^4+9x^3+5x^2+2x+4 [-11.99, 11.42, -1.56, 10.15]}