What are the solutions to the equation 4x^3-18x^2+24x=0 ?

The solutions to the equation 4x^3-18x^2+24x=0 are x=0,x= 9/4+i(sqrt(15))/4 ,x= 9/4-i(sqrt(15))/4

Find the zeros of 4x^3-18x^2+24x=0

The zeros of 4x^3-18x^2+24x=0 are x=0,x= 9/4+i(sqrt(15))/4 ,x= 9/4-i(sqrt(15))/4

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4 x^{3} - 18 x^{2} + 24 x = 0

x = 0, x = \frac{9}{4} + i \frac{15}{4}, x = \frac{9}{4} - i \frac{15}{4}

Solution steps

4 x^{3} - 18 x^{2} + 24 x = 0

Factor

4 x^{3} - 18 x^{2} + 24 x : 2 x (2 x^{2} - 9 x + 12)

2 x (2 x^{2} - 9 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x^{2} - 9 x + 12 = 0

Solve

2 x^{2} - 9 x + 12 = 0 : x = \frac{9}{4} + i \frac{15}{4}, x = \frac{9}{4} - i \frac{15}{4}

The solutions are

x = 0, x = \frac{9}{4} + i \frac{15}{4}, x = \frac{9}{4} - i \frac{15}{4}

x^{3} - 2 - 2 \times i = 0

4 x^{3} - 57 x^{2} + 252 x - 324 = 0

0 = c x (x - 1)^{2} - x

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

4 x^{4} = 0

What are the solutions to the equation 4x^3-18x^2+24x=0 ?
The solutions to the equation 4x^3-18x^2+24x=0 are x=0,x= 9/4+i(sqrt(15))/4 ,x= 9/4-i(sqrt(15))/4
Find the zeros of 4x^3-18x^2+24x=0
The zeros of 4x^3-18x^2+24x=0 are x=0,x= 9/4+i(sqrt(15))/4 ,x= 9/4-i(sqrt(15))/4