What are the solutions to the equation 27x^3-9x^2-12x+4=0 ?

The solutions to the equation 27x^3-9x^2-12x+4=0 are x= 1/3 ,x=-2/3 ,x= 2/3

Find the zeros of 27x^3-9x^2-12x+4=0

The zeros of 27x^3-9x^2-12x+4=0 are x= 1/3 ,x=-2/3 ,x= 2/3

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27 x^{3} - 9 x^{2} - 12 x + 4 = 0

x = \frac{1}{3}, x = - \frac{2}{3}, x = \frac{2}{3}

Decimal Notation

x = 0.33333 \dots, x = - 0.66666 \dots, x = 0.66666 \dots

Solution steps

27 x^{3} - 9 x^{2} - 12 x + 4 = 0

Factor

27 x^{3} - 9 x^{2} - 12 x + 4 : (3 x - 1) (3 x + 2) (3 x - 2)

(3 x - 1) (3 x + 2) (3 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x - 1 = 0 or 3 x + 2 = 0 or 3 x - 2 = 0

Solve

3 x - 1 = 0 : x = \frac{1}{3}

Solve

3 x + 2 = 0 : x = - \frac{2}{3}

Solve

3 x - 2 = 0 : x = \frac{2}{3}

The solutions are

x = \frac{1}{3}, x = - \frac{2}{3}, x = \frac{2}{3}

4 x^{3} + 15 x^{2} + 16 x + 6 = 0

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

g (n) = 3 n^{3} + 15 n^{2} + 5 n

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

x^{4} + 2 i x^{2} - 1 = 0

What are the solutions to the equation 27x^3-9x^2-12x+4=0 ?
The solutions to the equation 27x^3-9x^2-12x+4=0 are x= 1/3 ,x=-2/3 ,x= 2/3
Find the zeros of 27x^3-9x^2-12x+4=0
The zeros of 27x^3-9x^2-12x+4=0 are x= 1/3 ,x=-2/3 ,x= 2/3