Find all zeroes of the polynomial p(x)=3xpower 4-9x cube - x square+21x-14,if twonof the eroes are root 7 by 3 and - root 7 by 3
Answers
Roots
The
n
t
h
root of a number (a) is the number multiplied n times to find a.
In other words, if
b
n
=
a
, then
b
=
n
√
a
, where b is the
n
t
h
root of a.
Roots can also be defined through the concept of fractional/rational exponents.
Basic Root Rules
The following is a basic set of rules we use to solve problems involving fractional exponents/roots. Note that for the Root of 1 Rule, we are considering only positive 1. This is considered taking the "principal value" of the nth root.
Solving Root Problems
There is no "catch-all" way to solve root problems, but a general guideline can be helpful.
Apply the most obvious rule.
Factoring a term inside a root can help.
Look for perfect squares, perfect cubes, etc.
Simplify after every rule.
Solving Root Problems With Variables
Simplifying root problems with variables is no different than simplifying them with numbers. Here, we break down an algebraic expression with a variable, where
x
>
0
.