Use the Rational Roots Test to Find All Possible Roots f(x)=x^3-2x^2-25x+50

Problem

ƒ(x)=x3−2*x2−25*x+50

Solution

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

(a_0)=50

(a_n)=1

2. List all factors of the constant term (a_0)=50 which will be represented as p

p=±1,±2,±5,±10,±25,±50

3. List all factors of the leading coefficient (a_n)=1 which will be represented as q

q=±1

4. Apply the formula for the Rational Roots Test, which states that all possible rational roots are in the form p/q

p/q=(±1,±2,±5,±10,±25,±50)/(±1)

5. Simplify the list of possible roots by dividing each p by each q

Possible Roots=±1,±2,±5,±10,±25,±50

Final Answer

Possible Roots=±1,±2,±5,±10,±25,±50

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