What are the solutions to the equation 0=3x^4-8x^3+6x^2 ?

The solutions to the equation 0=3x^4-8x^3+6x^2 are x=0,x= 4/3+i(sqrt(2))/3 ,x= 4/3-i(sqrt(2))/3

Find the zeros of 0=3x^4-8x^3+6x^2

The zeros of 0=3x^4-8x^3+6x^2 are x=0,x= 4/3+i(sqrt(2))/3 ,x= 4/3-i(sqrt(2))/3

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0 = 3 x^{4} - 8 x^{3} + 6 x^{2}

x = 0, x = \frac{4}{3} + i \frac{2}{3}, x = \frac{4}{3} - i \frac{2}{3}

Solution steps

0 = 3 x^{4} - 8 x^{3} + 6 x^{2}

Switch sides

3 x^{4} - 8 x^{3} + 6 x^{2} = 0

Factor

3 x^{4} - 8 x^{3} + 6 x^{2} : x^{2} (3 x^{2} - 8 x + 6)

x^{2} (3 x^{2} - 8 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x^{2} - 8 x + 6 = 0

Solve

3 x^{2} - 8 x + 6 = 0 : x = \frac{4}{3} + i \frac{2}{3}, x = \frac{4}{3} - i \frac{2}{3}

The solutions are

x = 0, x = \frac{4}{3} + i \frac{2}{3}, x = \frac{4}{3} - i \frac{2}{3}

(z + 1)^{4} + 16 = 0

x^{3} + 4 x^{2} + 8 x = 0

3 = 0.03 x^{3} + 0.05 x^{2}

- 12 x^{5} - 6 x^{3} + 10 = 0

3 x^{3} - 33 x^{2} + 30 x = 0

What are the solutions to the equation 0=3x^4-8x^3+6x^2 ?
The solutions to the equation 0=3x^4-8x^3+6x^2 are x=0,x= 4/3+i(sqrt(2))/3 ,x= 4/3-i(sqrt(2))/3
Find the zeros of 0=3x^4-8x^3+6x^2
The zeros of 0=3x^4-8x^3+6x^2 are x=0,x= 4/3+i(sqrt(2))/3 ,x= 4/3-i(sqrt(2))/3