What are the solutions to the equation x^4+8x^3+8x^2+8x+7=0 ?

The solutions to the equation x^4+8x^3+8x^2+8x+7=0 are x=-1,x=-7,x=i,x=-i

Find the zeros of x^4+8x^3+8x^2+8x+7=0

The zeros of x^4+8x^3+8x^2+8x+7=0 are x=-1,x=-7,x=i,x=-i

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x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 = 0

x = - 1, x = - 7, x = i, x = - i

Solution steps

x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 = 0

Factor

x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 : (x + 1) (x + 7) (x^{2} + 1)

(x + 1) (x + 7) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x + 7 = 0 or x^{2} + 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x + 7 = 0 : x = - 7

Solve

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

The solutions are

x = - 1, x = - 7, x = i, x = - i

x^{3} - 9 x^{2} - 4 x + 36 = 0

x^{12} - x^{6} - 30 = 0

240 x^{3} + 360 x^{2} - 1800 x = 0

x^{3} - 2 x^{2} + 9 x - 18

125 = 40 x \frac{1}{2} (10) x^{2}

What are the solutions to the equation x^4+8x^3+8x^2+8x+7=0 ?
The solutions to the equation x^4+8x^3+8x^2+8x+7=0 are x=-1,x=-7,x=i,x=-i
Find the zeros of x^4+8x^3+8x^2+8x+7=0
The zeros of x^4+8x^3+8x^2+8x+7=0 are x=-1,x=-7,x=i,x=-i