# How do you use the rational roots theorem to find all possible zeros of # P(x) = 3x^4 + x^3 + 2x^2 - 2#?

##### 1 Answer

This quartic has no rational zeros, but we can find approximations:

#x_1 ~~ 0.694795#

#x_2 ~~ -0.800431#

#x_(3,4) ~~ -0.113849+-1.08894i#

#### Explanation:

#P(x) = 3x^4+x^3+2x^2-2#

By the rational root theorem and *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1/3, +-2/3, +-1, +-2#

None of these works, so *rational* zeros.

As a quartic, it is possible to solve

Here's a C++ program for this quartic...

Hence we can find approximations:

#x_1 ~~ 0.694795#

#x_2 ~~ -0.800431#

#x_(3,4) ~~ -0.113849+-1.08894i#