What are the solutions to the equation x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0 ?

The solutions to the equation x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0 are x=-2

Find the zeros of x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0

The zeros of x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0 are x=-2

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x^{9} + 2 x^{8} + 4 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 64 x^{3} + 128 x^{2} + 256 x + 512 = 0

x = - 2

Solution steps

x^{9} + 2 x^{8} + 4 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 64 x^{3} + 128 x^{2} + 256 x + 512 = 0

Factor

x^{9} + 2 x^{8} + 4 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 64 x^{3} + 128 x^{2} + 256 x + 512 : (x + 2) (x^{4} + 2 x^{3} + 4 x^{2} + 8 x + 16) (x^{4} - 2 x^{3} + 4 x^{2} - 8 x + 16)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

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

No Solution for

x \in R

Solve

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

No Solution for

x \in R

The solution is

x = - 2

m^{3} - 2 m^{2} - 4 m + 8 = 0

x^{3} = \frac{- 7}{2}

x^{4} + 3 x^{3} - 12 x^{2} + 2 x - 1 = 0

3 x^{3} + x - 10 = 0

x (x - 1) (x + 2)^{3} = 0

What are the solutions to the equation x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0 ?
The solutions to the equation x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0 are x=-2
Find the zeros of x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0
The zeros of x^9+2x^8+4x^7+8x^6+16x^5+32x^4+64x^3+128x^2+256x+512=0 are x=-2