What are the solutions to the equation y^5-12y^4+24y^3=0 ?

The solutions to the equation y^5-12y^4+24y^3=0 are y=0,y=2(3+sqrt(3)),y=2(3-sqrt(3))

Find the zeros of y^5-12y^4+24y^3=0

The zeros of y^5-12y^4+24y^3=0 are y=0,y=2(3+sqrt(3)),y=2(3-sqrt(3))

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y^{5} - 12 y^{4} + 24 y^{3} = 0

y = 0, y = 2 (3 + 3), y = 2 (3 - 3)

Decimal Notation

y = 0, y = 9.46410 \dots, y = 2.53589 \dots

Solution steps

y^{5} - 12 y^{4} + 24 y^{3} = 0

Factor

y^{5} - 12 y^{4} + 24 y^{3} : y^{3} (y^{2} - 12 y + 24)

y^{3} (y^{2} - 12 y + 24) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y^{2} - 12 y + 24 = 0

Solve

y^{2} - 12 y + 24 = 0 : y = 2 (3 + 3), y = 2 (3 - 3)

The solutions are

y = 0, y = 2 (3 + 3), y = 2 (3 - 3)

x, x^{3} + 2 x^{2} + x = 0

s^{3} = 27

17 c^{1} + 5 c^{2} + 255 c^{3} = 53

x^{4} - x^{3} + 4 x^{2} - 4 x = 0

(2 x + 2) (3 x - 6) (4 x + 12) = 0

What are the solutions to the equation y^5-12y^4+24y^3=0 ?
The solutions to the equation y^5-12y^4+24y^3=0 are y=0,y=2(3+sqrt(3)),y=2(3-sqrt(3))
Find the zeros of y^5-12y^4+24y^3=0
The zeros of y^5-12y^4+24y^3=0 are y=0,y=2(3+sqrt(3)),y=2(3-sqrt(3))