What are the solutions to the equation y^5-16y^4+14y^3=0 ?

The solutions to the equation y^5-16y^4+14y^3=0 are y=0,y=8+5sqrt(2),y=8-5sqrt(2)

Find the zeros of y^5-16y^4+14y^3=0

The zeros of y^5-16y^4+14y^3=0 are y=0,y=8+5sqrt(2),y=8-5sqrt(2)

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y^{5} - 16 y^{4} + 14 y^{3} = 0

y = 0, y = 8 + 52, y = 8 - 52

Decimal Notation

y = 0, y = 15.07106 \dots, y = 0.92893 \dots

Solution steps

y^{5} - 16 y^{4} + 14 y^{3} = 0

Factor

y^{5} - 16 y^{4} + 14 y^{3} : y^{3} (y^{2} - 16 y + 14)

y^{3} (y^{2} - 16 y + 14) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y^{2} - 16 y + 14 = 0

Solve

y^{2} - 16 y + 14 = 0 : y = 8 + 52, y = 8 - 52

The solutions are

y = 0, y = 8 + 52, y = 8 - 52

x^{3} - 6 x - 26 = 0

500 x - 500 x^{3} = 96

2 x^{3} + 5 x^{2} - 36 x = 90

x, y^{3} - x^{3} = 3

b^{3} = 5

What are the solutions to the equation y^5-16y^4+14y^3=0 ?
The solutions to the equation y^5-16y^4+14y^3=0 are y=0,y=8+5sqrt(2),y=8-5sqrt(2)
Find the zeros of y^5-16y^4+14y^3=0
The zeros of y^5-16y^4+14y^3=0 are y=0,y=8+5sqrt(2),y=8-5sqrt(2)