Find the Roots (Zeros) f(x)=x^4-3x^3-20x^2

Problem

ƒ(x)=x^4−3*x^3−20*x^2

Solution

1. Set the function to zero to find the roots of the equation.

x^4−3*x^3−20*x^2=0

2. Factor out the greatest common factor, which is x^2

x^2*(x^2−3*x−20)=0

3. Identify the roots from the first factor by setting x^2=0

x=0

4. Apply the quadratic formula to the remaining quadratic expression x^2−3*x−20=0 where a=1 b=−3 and c=−20

x=(−(−3)±√(,(−3)^2−4*(1)*(−20)))/(2*(1))

5. Simplify the discriminant and the expression to find the remaining roots.

x=(3±√(,9+80))/2

x=(3±√(,89))/2

Final Answer

x=0,(3+√(,89))/2,(3−√(,89))/2

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