Use the Rational Roots Test to Find All Possible Roots f(x)

Problem

ƒ(x)=2*x3+3*x2−8*x+3

Solution

1. Identify the constant term and the leading coefficient of the polynomial.

(a_0)=3

(a_n)=2

2. List all factors of the constant term (a_0)=3 which represent the possible values for the numerator p

p∈{±1,±3}

3. List all factors of the leading coefficient (a_n)=2 which represent the possible values for the denominator q

q∈{1,2}

4. Determine all possible rational roots by forming the ratios p/q

p/q∈{±1/1,±3/1,±1/2,±3/2}

5. Simplify the list of ratios to find the unique possible roots.

Possible Roots∈{±1,±3,±1/2,±3/2}

Final Answer

Possible Roots=±1,±3,±1/2,±3/2

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