What are the solutions to the equation 4x^3-24x^2+48x=0 ?

The solutions to the equation 4x^3-24x^2+48x=0 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i

Find the zeros of 4x^3-24x^2+48x=0

The zeros of 4x^3-24x^2+48x=0 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i

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4 x^{3} - 24 x^{2} + 48 x = 0

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

Solution steps

4 x^{3} - 24 x^{2} + 48 x = 0

Factor

4 x^{3} - 24 x^{2} + 48 x : 4 x (x^{2} - 6 x + 12)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 6 x + 12 = 0

Solve

x^{2} - 6 x + 12 = 0 : x = 3 + 3 i, x = 3 - 3 i

The solutions are

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

9 x^{3} + 45 x^{2} + 59 x + 15

64 m = m^{3} - m^{2} + m - 62

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

2 x^{2} + 5 = (x^{2} + 1)^{2}

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

What are the solutions to the equation 4x^3-24x^2+48x=0 ?
The solutions to the equation 4x^3-24x^2+48x=0 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i
Find the zeros of 4x^3-24x^2+48x=0
The zeros of 4x^3-24x^2+48x=0 are x=0,x=3+sqrt(3)i,x=3-sqrt(3)i