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

The solutions to the equation 2x^3+5x+7=0 are x=-1,x= 1/2+i(sqrt(13))/2 ,x= 1/2-i(sqrt(13))/2

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

The zeros of 2x^3+5x+7=0 are x=-1,x= 1/2+i(sqrt(13))/2 ,x= 1/2-i(sqrt(13))/2

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

x = - 1, x = \frac{1}{2} + i \frac{13}{2}, x = \frac{1}{2} - i \frac{13}{2}

Solution steps

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

Factor

2 x^{3} + 5 x + 7 : (x + 1) (2 x^{2} - 2 x + 7)

(x + 1) (2 x^{2} - 2 x + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or 2 x^{2} - 2 x + 7 = 0

Solve

x + 1 = 0 : x = - 1

Solve

2 x^{2} - 2 x + 7 = 0 : x = \frac{1}{2} + i \frac{13}{2}, x = \frac{1}{2} - i \frac{13}{2}

The solutions are

x = - 1, x = \frac{1}{2} + i \frac{13}{2}, x = \frac{1}{2} - i \frac{13}{2}

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

x^{3} + 12 x^{2} + 29 \cdot + 18 = 0

4 z (z^{2} - 5) = 4 z^{2} - 27

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

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

What are the solutions to the equation 2x^3+5x+7=0 ?
The solutions to the equation 2x^3+5x+7=0 are x=-1,x= 1/2+i(sqrt(13))/2 ,x= 1/2-i(sqrt(13))/2
Find the zeros of 2x^3+5x+7=0
The zeros of 2x^3+5x+7=0 are x=-1,x= 1/2+i(sqrt(13))/2 ,x= 1/2-i(sqrt(13))/2