What are the solutions to the equation x^4+8x^3+17x^2+8x+16=0 ?

The solutions to the equation x^4+8x^3+17x^2+8x+16=0 are x=-4,x=i,x=-i

Find the zeros of x^4+8x^3+17x^2+8x+16=0

The zeros of x^4+8x^3+17x^2+8x+16=0 are x=-4,x=i,x=-i

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x^{4} + 8 x^{3} + 17 x^{2} + 8 x + 16 = 0

x = - 4, x = i, x = - i

Solution steps

x^{4} + 8 x^{3} + 17 x^{2} + 8 x + 16 = 0

Factor

x^{4} + 8 x^{3} + 17 x^{2} + 8 x + 16 : (x + 4)^{2} (x^{2} + 1)

(x + 4)^{2} (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 4 = 0 or x^{2} + 1 = 0

Solve

x + 4 = 0 : x = - 4

Solve

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

The solutions are

x = - 4, x = i, x = - i

x^{4} + 12 x + 3 = 0

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

z^{8} - 2 z^{4} + 4 = 0

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

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

What are the solutions to the equation x^4+8x^3+17x^2+8x+16=0 ?
The solutions to the equation x^4+8x^3+17x^2+8x+16=0 are x=-4,x=i,x=-i
Find the zeros of x^4+8x^3+17x^2+8x+16=0
The zeros of x^4+8x^3+17x^2+8x+16=0 are x=-4,x=i,x=-i