What are the solutions to the equation 4t^3+4t^2-2t=0 ?

The solutions to the equation 4t^3+4t^2-2t=0 are t=0,t=(-1+sqrt(3))/2 ,t=-(1+sqrt(3))/2

Find the zeros of 4t^3+4t^2-2t=0

The zeros of 4t^3+4t^2-2t=0 are t=0,t=(-1+sqrt(3))/2 ,t=-(1+sqrt(3))/2

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

t = 0, t = \frac{- 1 + 3}{2}, t = - \frac{1 + 3}{2}

Decimal Notation

t = 0, t = 0.36602 \dots, t = - 1.36602 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

t = 0, t = \frac{- 1 + 3}{2}, t = - \frac{1 + 3}{2}

2 x^{4} + 17 x^{3} + 43 x^{2} + 37 x + 6 = 0

4 x^{4} - 13 x + 3 = 0

- 4 x^{3} + 6 x^{2} = 0

2 x (x^{2} + 3) = 0

8 x^{6} + 7 x^{3} - 1 = 0

What are the solutions to the equation 4t^3+4t^2-2t=0 ?
The solutions to the equation 4t^3+4t^2-2t=0 are t=0,t=(-1+sqrt(3))/2 ,t=-(1+sqrt(3))/2
Find the zeros of 4t^3+4t^2-2t=0
The zeros of 4t^3+4t^2-2t=0 are t=0,t=(-1+sqrt(3))/2 ,t=-(1+sqrt(3))/2