What are the solutions to the equation 5x^5=-40x^2 ?

The solutions to the equation 5x^5=-40x^2 are x=0,x=-2,x=1+sqrt(3)i,x=1-sqrt(3)i

Find the zeros of 5x^5=-40x^2

The zeros of 5x^5=-40x^2 are x=0,x=-2,x=1+sqrt(3)i,x=1-sqrt(3)i

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5 x^{5} = - 40 x^{2}

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

Solution steps

5 x^{5} = - 40 x^{2}

Move

40 x^{2}

to the left side

5 x^{5} + 40 x^{2} = 0

Factor

5 x^{5} + 40 x^{2} : 5 x^{2} (x + 2) (x^{2} - 2 x + 4)

5 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

λ^{3} - 3 λ^{2} + 3 λ - 1 = 0

12 q - 21 q^{2} - 6 q^{3} = 0

5 - 1 x^{3} = - 15

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

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

What are the solutions to the equation 5x^5=-40x^2 ?
The solutions to the equation 5x^5=-40x^2 are x=0,x=-2,x=1+sqrt(3)i,x=1-sqrt(3)i
Find the zeros of 5x^5=-40x^2
The zeros of 5x^5=-40x^2 are x=0,x=-2,x=1+sqrt(3)i,x=1-sqrt(3)i