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

The solutions to the equation 3x^2-4x^3+12x=0 are x=0,x=(3+sqrt(201))/8 ,x=(3-sqrt(201))/8

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

The zeros of 3x^2-4x^3+12x=0 are x=0,x=(3+sqrt(201))/8 ,x=(3-sqrt(201))/8

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

x = 0, x = \frac{3 + 201}{8}, x = \frac{3 - 201}{8}

Decimal Notation

x = 0, x = 2.14718 \dots, x = - 1.39718 \dots

Solution steps

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

Factor

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

- x (4 x^{2} - 3 x - 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

4 x^{2} - 3 x - 12 = 0 : x = \frac{3 + 201}{8}, x = \frac{3 - 201}{8}

The solutions are

x = 0, x = \frac{3 + 201}{8}, x = \frac{3 - 201}{8}

x^{3} - 21 x - 20 = 0

y^{4} - 17 y^{2} + 16 = 0

4 x^{4} - 9 x^{2} = 0

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

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

What are the solutions to the equation 3x^2-4x^3+12x=0 ?
The solutions to the equation 3x^2-4x^3+12x=0 are x=0,x=(3+sqrt(201))/8 ,x=(3-sqrt(201))/8
Find the zeros of 3x^2-4x^3+12x=0
The zeros of 3x^2-4x^3+12x=0 are x=0,x=(3+sqrt(201))/8 ,x=(3-sqrt(201))/8