What are the solutions to the equation x^3+5x^2+7x=0 ?

The solutions to the equation x^3+5x^2+7x=0 are x=0,x=-5/2+i(sqrt(3))/2 ,x=-5/2-i(sqrt(3))/2

Find the zeros of x^3+5x^2+7x=0

The zeros of x^3+5x^2+7x=0 are x=0,x=-5/2+i(sqrt(3))/2 ,x=-5/2-i(sqrt(3))/2

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x^{3} + 5 x^{2} + 7 x = 0

x = 0, x = - \frac{5}{2} + i \frac{3}{2}, x = - \frac{5}{2} - i \frac{3}{2}

Solution steps

x^{3} + 5 x^{2} + 7 x = 0

Factor

x^{3} + 5 x^{2} + 7 x : x (x^{2} + 5 x + 7)

x (x^{2} + 5 x + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} + 5 x + 7 = 0

Solve

x^{2} + 5 x + 7 = 0 : x = - \frac{5}{2} + i \frac{3}{2}, x = - \frac{5}{2} - i \frac{3}{2}

The solutions are

x = 0, x = - \frac{5}{2} + i \frac{3}{2}, x = - \frac{5}{2} - i \frac{3}{2}

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

4 x^{3} + 12 x^{2} + 16 x = 0

x^{4} - 6 x^{3} + 6 x^{2} - 6 x + 5 = 0

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

z, (a) z^{4} = 24 i - 7

What are the solutions to the equation x^3+5x^2+7x=0 ?
The solutions to the equation x^3+5x^2+7x=0 are x=0,x=-5/2+i(sqrt(3))/2 ,x=-5/2-i(sqrt(3))/2
Find the zeros of x^3+5x^2+7x=0
The zeros of x^3+5x^2+7x=0 are x=0,x=-5/2+i(sqrt(3))/2 ,x=-5/2-i(sqrt(3))/2