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

The solutions to the equation x^2-3x^3+2=0 are x=1,x=-1/3+i(sqrt(5))/3 ,x=-1/3-i(sqrt(5))/3

Find the zeros of x^2-3x^3+2=0

The zeros of x^2-3x^3+2=0 are x=1,x=-1/3+i(sqrt(5))/3 ,x=-1/3-i(sqrt(5))/3

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

x = 1, x = - \frac{1}{3} + i \frac{5}{3}, x = - \frac{1}{3} - i \frac{5}{3}

Solution steps

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

Write in the standard form

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

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

Factor

- 3 x^{3} + x^{2} + 2 : - (x - 1) (3 x^{2} + 2 x + 2)

- (x - 1) (3 x^{2} + 2 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 3 x^{2} + 2 x + 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

3 x^{2} + 2 x + 2 = 0 : x = - \frac{1}{3} + i \frac{5}{3}, x = - \frac{1}{3} - i \frac{5}{3}

The solutions are

x = 1, x = - \frac{1}{3} + i \frac{5}{3}, x = - \frac{1}{3} - i \frac{5}{3}

a^{3} = - 64

16 x^{4} - 1321 x^{2} + 2025 = 0

y (y - 2)^{2} = 0

31 = 4 (x^{2} + 2)^{3} - 1

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

What are the solutions to the equation x^2-3x^3+2=0 ?
The solutions to the equation x^2-3x^3+2=0 are x=1,x=-1/3+i(sqrt(5))/3 ,x=-1/3-i(sqrt(5))/3
Find the zeros of x^2-3x^3+2=0
The zeros of x^2-3x^3+2=0 are x=1,x=-1/3+i(sqrt(5))/3 ,x=-1/3-i(sqrt(5))/3