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

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

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

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

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

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

Solution steps

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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}

- 247 b^{2} + 15 b^{4} = 0

133 = 137 (1 + r)^{10}

- x^{4} + 27 x^{2} - 10 x = 0

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

2 x^{5} - 12 x^{3} = 0

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