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Give all possible rational zero for the following polynomial. P(x) = 6x3 + 24x2 + 2x - 3

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.4: Zeros Of Polynomial Functions

Problem 2ECP

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Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

Give all possible rational zero for the following polynomial.
P(x) = 6x³ + 24x² + 2x - 3

Expert Solution

Step 1

Give all possible rational zero for the following polynomial.

Step 2

Here we find the all possible rational roots.

We use the concept of Rational root test.

It state that,

Suppose we have some polynomial $P(x)P\left( x \right)$ with integer coefficients and a nonzero constant term:

f(x) a"a
+...+ajx+a
here
a0
&
Then every rational root of fx) is of the form
p_+(factors of a)
q +(factors of a,

Step 3

Factors of -3 is p

factors of 6 is q.

Step by step

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