What are the solutions to the equation y^5-14y^4+4y^3=0 ?

The solutions to the equation y^5-14y^4+4y^3=0 are y=0,y=7+3sqrt(5),y=7-3sqrt(5)

Find the zeros of y^5-14y^4+4y^3=0

The zeros of y^5-14y^4+4y^3=0 are y=0,y=7+3sqrt(5),y=7-3sqrt(5)

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y^{5} - 14 y^{4} + 4 y^{3} = 0

y = 0, y = 7 + 35, y = 7 - 35

Decimal

y = 0, y = 13.70820 \dots, y = 0.29179 \dots

Solution steps

y^{5} - 14 y^{4} + 4 y^{3} = 0

Factor

y^{5} - 14 y^{4} + 4 y^{3} : y^{3} (y^{2} - 14 y + 4)

y^{3} (y^{2} - 14 y + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y^{2} - 14 y + 4 = 0

Solve

y^{2} - 14 y + 4 = 0 : y = 7 + 35, y = 7 - 35

The solutions are

y = 0, y = 7 + 35, y = 7 - 35

x^{3} = 8000

x + 2 = 1.21 x^{10}

16 x^{4} + 65 x^{2} + 4 = 0

y^{4} + 7 y^{2} + 6 y = 0

x^{3} - 3 x^{2} + 5 x - 3 = 0

What are the solutions to the equation y^5-14y^4+4y^3=0 ?
The solutions to the equation y^5-14y^4+4y^3=0 are y=0,y=7+3sqrt(5),y=7-3sqrt(5)
Find the zeros of y^5-14y^4+4y^3=0
The zeros of y^5-14y^4+4y^3=0 are y=0,y=7+3sqrt(5),y=7-3sqrt(5)