What are the solutions to the equation y^5-18y^4+69y^3=0 ?

The solutions to the equation y^5-18y^4+69y^3=0 are y=0,y=9+2sqrt(3),y=9-2sqrt(3)

Find the zeros of y^5-18y^4+69y^3=0

The zeros of y^5-18y^4+69y^3=0 are y=0,y=9+2sqrt(3),y=9-2sqrt(3)

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y^{5} - 18 y^{4} + 69 y^{3} = 0

y = 0, y = 9 + 23, y = 9 - 23

Decimal Notation

y = 0, y = 12.46410 \dots, y = 5.53589 \dots

Solution steps

y^{5} - 18 y^{4} + 69 y^{3} = 0

Factor

y^{5} - 18 y^{4} + 69 y^{3} : y^{3} (y^{2} - 18 y + 69)

y^{3} (y^{2} - 18 y + 69) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y^{2} - 18 y + 69 = 0

Solve

y^{2} - 18 y + 69 = 0 : y = 9 + 23, y = 9 - 23

The solutions are

y = 0, y = 9 + 23, y = 9 - 23

x^{3} - 9 x^{2} + 24 x - 8 = 0

x^{2} + (x^{2} - 4)^{2} = 16

x^{6} = 256

6 j^{4} = 96

2 x^{4} + 7 x^{2} - 225 = 0

What are the solutions to the equation y^5-18y^4+69y^3=0 ?
The solutions to the equation y^5-18y^4+69y^3=0 are y=0,y=9+2sqrt(3),y=9-2sqrt(3)
Find the zeros of y^5-18y^4+69y^3=0
The zeros of y^5-18y^4+69y^3=0 are y=0,y=9+2sqrt(3),y=9-2sqrt(3)