What are the solutions to the equation 4x^3-15x^2+12x=0 ?

The solutions to the equation 4x^3-15x^2+12x=0 are x=0,x=(15+sqrt(33))/8 ,x=(15-sqrt(33))/8

Find the zeros of 4x^3-15x^2+12x=0

The zeros of 4x^3-15x^2+12x=0 are x=0,x=(15+sqrt(33))/8 ,x=(15-sqrt(33))/8

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4 x^{3} - 15 x^{2} + 12 x = 0

x = 0, x = \frac{15 + 33}{8}, x = \frac{15 - 33}{8}

Decimal Notation

x = 0, x = 2.59307 \dots, x = 1.15692 \dots

Solution steps

4 x^{3} - 15 x^{2} + 12 x = 0

Factor

4 x^{3} - 15 x^{2} + 12 x : x (4 x^{2} - 15 x + 12)

x (4 x^{2} - 15 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 x^{2} - 15 x + 12 = 0

Solve

4 x^{2} - 15 x + 12 = 0 : x = \frac{15 + 33}{8}, x = \frac{15 - 33}{8}

The solutions are

x = 0, x = \frac{15 + 33}{8}, x = \frac{15 - 33}{8}

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

x^{7} = - 128

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

x^{4} + 3 x^{2} = 10

12 x^{3} - 91 x^{2} + 50 x - 7 = 0

What are the solutions to the equation 4x^3-15x^2+12x=0 ?
The solutions to the equation 4x^3-15x^2+12x=0 are x=0,x=(15+sqrt(33))/8 ,x=(15-sqrt(33))/8
Find the zeros of 4x^3-15x^2+12x=0
The zeros of 4x^3-15x^2+12x=0 are x=0,x=(15+sqrt(33))/8 ,x=(15-sqrt(33))/8