Solve for y y^5-18y^4+6y^3=0

Problem

y^5−18*y^4+6*y^3=0

Solution

1. Identify the greatest common factor in all terms of the polynomial.

2. Factor out the common term y^3 from the expression.

y^3*(y^2−18*y+6)=0

3. Apply the zero product property, setting each factor equal to zero.

y^3=0

y^2−18*y+6=0

4. Solve the first equation for y

y=0

5. Apply the quadratic formula y=(−b±√(,b^2−4*a*c))/(2*a) to the second equation, where a=1 b=−18 and c=6

y=(−(−18)±√(,(−18)^2−4*(1)*(6)))/(2*(1))

6. Simplify the expression under the square root.

y=(18±√(,324−24))/2

y=(18±√(,300))/2

7. Simplify the radical √(,300) as 10√(,3)

y=(18±10√(,3))/2

8. Divide both terms in the numerator by 2 to find the remaining roots.

y=9±5√(,3)

Final Answer

y=0,9+5√(,3),9−5√(,3)

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