What are the solutions to the equation x^4+2x^3-8x-16=0 ?

The solutions to the equation x^4+2x^3-8x-16=0 are x=-2,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

Find the zeros of x^4+2x^3-8x-16=0

The zeros of x^4+2x^3-8x-16=0 are x=-2,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

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x^{4} + 2 x^{3} - 8 x - 16 = 0

x = - 2, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Solution steps

x^{4} + 2 x^{3} - 8 x - 16 = 0

Factor

x^{4} + 2 x^{3} - 8 x - 16 : (x + 2) (x - 2) (x^{2} + 2 x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 2 x + 4 = 0 : x = - 1 + 3 i, x = - 1 - 3 i

The solutions are

x = - 2, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

(3 x - 4)^{10} - 3 = 1021

(3 x^{4})^{5} = (3^{3})^{3}

3 \frac{x}{5} - \frac{1}{4} = x^{7} \frac{x}{10} - \frac{1}{5}

5 x^{4} + 2 x^{3} - 1 = 0

(x + 2)^{3} = 2 \cdot x \cdot (x^{2} - 1)

What are the solutions to the equation x^4+2x^3-8x-16=0 ?
The solutions to the equation x^4+2x^3-8x-16=0 are x=-2,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i
Find the zeros of x^4+2x^3-8x-16=0
The zeros of x^4+2x^3-8x-16=0 are x=-2,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i