What are the solutions to the equation t^3-6t^2=2t ?

The solutions to the equation t^3-6t^2=2t are t=0,t=3+sqrt(11),t=3-sqrt(11)

Find the zeros of t^3-6t^2=2t

The zeros of t^3-6t^2=2t are t=0,t=3+sqrt(11),t=3-sqrt(11)

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t^{3} - 6 t^{2} = 2 t

t = 0, t = 3 + 11, t = 3 - 11

Decimal Notation

t = 0, t = 6.31662 \dots, t = - 0.31662 \dots

Solution steps

t^{3} - 6 t^{2} = 2 t

Move

2 t

to the left side

t^{3} - 6 t^{2} - 2 t = 0

Factor

t^{3} - 6 t^{2} - 2 t : t (t^{2} - 6 t - 2)

t (t^{2} - 6 t - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t = 0 or t^{2} - 6 t - 2 = 0

Solve

t^{2} - 6 t - 2 = 0 : t = 3 + 11, t = 3 - 11

The solutions are

t = 0, t = 3 + 11, t = 3 - 11

63 x - 2 x^{2} - x^{3} = 0

x^{5} = 1024

4 x^{5} - x^{3} - 4 x^{2} + 1 = 0

x^{4} - 5 x^{2} - 44 = 0

(x - 5)^{3} = 1

What are the solutions to the equation t^3-6t^2=2t ?
The solutions to the equation t^3-6t^2=2t are t=0,t=3+sqrt(11),t=3-sqrt(11)
Find the zeros of t^3-6t^2=2t
The zeros of t^3-6t^2=2t are t=0,t=3+sqrt(11),t=3-sqrt(11)