What are the solutions to the equation 0=x^3+4x-5 ?

The solutions to the equation 0=x^3+4x-5 are x=1,x=-1/2+i(sqrt(19))/2 ,x=-1/2-i(sqrt(19))/2

Find the zeros of 0=x^3+4x-5

The zeros of 0=x^3+4x-5 are x=1,x=-1/2+i(sqrt(19))/2 ,x=-1/2-i(sqrt(19))/2

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

x = 1, x = - \frac{1}{2} + i \frac{19}{2}, x = - \frac{1}{2} - i \frac{19}{2}

Solution steps

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

Switch sides

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

Factor

x^{3} + 4 x - 5 : (x - 1) (x^{2} + x + 5)

(x - 1) (x^{2} + x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + x + 5 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 5 = 0 : x = - \frac{1}{2} + i \frac{19}{2}, x = - \frac{1}{2} - i \frac{19}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{19}{2}, x = - \frac{1}{2} - i \frac{19}{2}

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

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

(x - 1)^{3} = (x - 1)^{2}

4 x^{4} + 17 x^{2} + 4 = 0

27 x^{4} + 21 x^{2} + 4 = 0

What are the solutions to the equation 0=x^3+4x-5 ?
The solutions to the equation 0=x^3+4x-5 are x=1,x=-1/2+i(sqrt(19))/2 ,x=-1/2-i(sqrt(19))/2
Find the zeros of 0=x^3+4x-5
The zeros of 0=x^3+4x-5 are x=1,x=-1/2+i(sqrt(19))/2 ,x=-1/2-i(sqrt(19))/2