Find the Roots/Zeros Using the Rational Roots Test x^3-2x^2-25x+50

Problem

x3−2*x2−25*x+50

Solution

1. Identify the constant term (a_0)=50 and the leading coefficient (a_n)=1

2. List all possible factors of the constant term p and the leading coefficient q

p:±1,±2,±5,±10,±25,±50

q:±1

3. Determine the possible rational roots p/q by dividing the factors of p by the factors of q

p/q:±1,±2,±5,±10,±25,±50

4. Test the possible roots using synthetic division or substitution. Testing x=2

2−2*(2)−25*(2)+50=8−8−50+50=0

⇒(x−2)* is a factor.

5. Divide the polynomial by (x−2) to find the remaining quadratic factor.

(x3−2*x2−25*x+50)÷(x−2)=x2−25

6. Solve the resulting quadratic equation x2−25=0 to find the remaining roots.

x2=25

x=±5

Final Answer

x=2,5,−5

Want more problems? Check here!