What are the solutions to the equation 1-3t^2-3t+t^3=0 ?

The solutions to the equation 1-3t^2-3t+t^3=0 are t=-1,t=2+sqrt(3),t=2-sqrt(3)

Find the zeros of 1-3t^2-3t+t^3=0

The zeros of 1-3t^2-3t+t^3=0 are t=-1,t=2+sqrt(3),t=2-sqrt(3)

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1 - 3 t^{2} - 3 t + t^{3} = 0

t = - 1, t = 2 + 3, t = 2 - 3

Decimal Notation

t = - 1, t = 3.73205 \dots, t = 0.26794 \dots

Solution steps

1 - 3 t^{2} - 3 t + t^{3} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

t^{3} - 3 t^{2} - 3 t + 1 = 0

Factor

t^{3} - 3 t^{2} - 3 t + 1 : (t + 1) (t^{2} - 4 t + 1)

(t + 1) (t^{2} - 4 t + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t + 1 = 0 or t^{2} - 4 t + 1 = 0

Solve

t + 1 = 0 : t = - 1

Solve

t^{2} - 4 t + 1 = 0 : t = 2 + 3, t = 2 - 3

The solutions are

t = - 1, t = 2 + 3, t = 2 - 3

20 x^{4} - 5 x^{3} - 12 x^{2} + 3 x = 0

2 x^{3} + 2 x^{2} - 8 x + 12 = 0

x^{4} + 16 = 0

n^{3} - 3 n^{2} + 2 n - 336 = 0

x, x^{3} - y^{3} + z^{3} = 4

What are the solutions to the equation 1-3t^2-3t+t^3=0 ?
The solutions to the equation 1-3t^2-3t+t^3=0 are t=-1,t=2+sqrt(3),t=2-sqrt(3)
Find the zeros of 1-3t^2-3t+t^3=0
The zeros of 1-3t^2-3t+t^3=0 are t=-1,t=2+sqrt(3),t=2-sqrt(3)