What are the solutions to the equation 3x^5=24x^2 ?

The solutions to the equation 3x^5=24x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

Find the zeros of 3x^5=24x^2

The zeros of 3x^5=24x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

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3 x^{5} = 24 x^{2}

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Solution steps

3 x^{5} = 24 x^{2}

Move

24 x^{2}

to the left side

3 x^{5} - 24 x^{2} = 0

Factor

3 x^{5} - 24 x^{2} : 3 x^{2} (x - 2) (x^{2} + 2 x + 4)

3 x^{2} (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 = 0 or x^{2} + 2 x + 4 = 0

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

- x^{3} + 5 x^{2} - 6 x = 0

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

(x^{2} + 1)^{2} = 0

x^{4} + 10 x^{2} + 9 = 0

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

What are the solutions to the equation 3x^5=24x^2 ?
The solutions to the equation 3x^5=24x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i
Find the zeros of 3x^5=24x^2
The zeros of 3x^5=24x^2 are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i