What are the solutions to the equation 3x^4+12x^2=6x^3 ?

The solutions to the equation 3x^4+12x^2=6x^3 are x=0,x=1+sqrt(3)i,x=1-sqrt(3)i

Find the zeros of 3x^4+12x^2=6x^3

The zeros of 3x^4+12x^2=6x^3 are x=0,x=1+sqrt(3)i,x=1-sqrt(3)i

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3 x^{4} + 12 x^{2} = 6 x^{3}

x = 0, x = 1 + 3 i, x = 1 - 3 i

Solution steps

3 x^{4} + 12 x^{2} = 6 x^{3}

Move

6 x^{3}

to the left side

3 x^{4} + 12 x^{2} - 6 x^{3} = 0

Factor

3 x^{4} + 12 x^{2} - 6 x^{3} : 3 x^{2} (x^{2} - 2 x + 4)

3 x^{2} (x^{2} - 2 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 2 x + 4 = 0

Solve

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

The solutions are

x = 0, x = 1 + 3 i, x = 1 - 3 i

x^{3} + x^{2} = 1

(m + 1)^{3} = 0

2 x^{3} - 250 = 0

x^{4} - 8 x^{2} + 16 = 0

5 x^{5} - 44 x^{3} - 9 x = 0

What are the solutions to the equation 3x^4+12x^2=6x^3 ?
The solutions to the equation 3x^4+12x^2=6x^3 are x=0,x=1+sqrt(3)i,x=1-sqrt(3)i
Find the zeros of 3x^4+12x^2=6x^3
The zeros of 3x^4+12x^2=6x^3 are x=0,x=1+sqrt(3)i,x=1-sqrt(3)i