What are the solutions to the equation x^3+3x+4=0 ?

The solutions to the equation x^3+3x+4=0 are x=-1,x= 1/2+i(sqrt(15))/2 ,x= 1/2-i(sqrt(15))/2

Find the zeros of x^3+3x+4=0

The zeros of x^3+3x+4=0 are x=-1,x= 1/2+i(sqrt(15))/2 ,x= 1/2-i(sqrt(15))/2

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

x = - 1, x = \frac{1}{2} + i \frac{15}{2}, x = \frac{1}{2} - i \frac{15}{2}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - x + 4 = 0 : x = \frac{1}{2} + i \frac{15}{2}, x = \frac{1}{2} - i \frac{15}{2}

The solutions are

x = - 1, x = \frac{1}{2} + i \frac{15}{2}, x = \frac{1}{2} - i \frac{15}{2}

x^{4} - 6 x^{2} - 7 = 0

x^{8} + 48 x^{4} - 49 = 0

x^{3} + x + 5 = 0

18 x^{4} + 6 x^{3} - 24 x^{2} - 8 x = 0

x^{4} - 3 x^{3} - 3 x^{2} + 7 x + 6 = 0

What are the solutions to the equation x^3+3x+4=0 ?
The solutions to the equation x^3+3x+4=0 are x=-1,x= 1/2+i(sqrt(15))/2 ,x= 1/2-i(sqrt(15))/2
Find the zeros of x^3+3x+4=0
The zeros of x^3+3x+4=0 are x=-1,x= 1/2+i(sqrt(15))/2 ,x= 1/2-i(sqrt(15))/2