What are the solutions to the equation x^4-2x^2-3x-2=0 ?

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

Find the zeros of x^4-2x^2-3x-2=0

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

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

x = - 1, x = 2, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

The solutions are

x = - 1, x = 2, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 = 0

x^{3} - 5 x^{2} = - 4 x

3 x^{6} - 14 x^{3} = 80

6 x^{2} x = 2

x^{8} = xx + 5

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