Use the Rational Roots Test to Find All Possible Roots f(x)=5x^3-7x^2-45x+63

Problem

ƒ(x)=5*x3−7*x2−45*x+63

Solution

1. Identify the constant term (a_0) and the leading coefficient (a_n)

(a_0)=63

(a_n)=5

2. List all factors of the constant term (a_0)=63 which will be represented as p

p=±1,±3,±7,±9,±21,±63

3. List all factors of the leading coefficient (a_n)=5 which will be represented as q

q=±1,±5

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

p/q=±(1,3,7,9,21,63)/(1,5)

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

p/q=±1,±3,±7,±9,±21,±63,±1/5,±3/5,±7/5,±9/5,±21/5,±63/5

Final Answer

Possible Roots=±1,±3,±7,±9,±21,±63,±1/5,±3/5,±7/5,±9/5,±21/5,±63/5

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