What are the solutions to the equation x^4+3x^3+3x^2+2x+1=0 ?

The solutions to the equation x^4+3x^3+3x^2+2x+1=0 are x=-1,x\approx-1.75487…

Find the zeros of x^4+3x^3+3x^2+2x+1=0

The zeros of x^4+3x^3+3x^2+2x+1=0 are x=-1,x\approx-1.75487…

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

x = - 1, x \approx - 1.75487 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{3} + 2 x^{2} + x + 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{3} + 2 x^{2} + x + 1 = 0 : x \approx - 1.75487 \dots

The solutions are

x = - 1, x \approx - 1.75487 \dots

2 x + 4 = x^{3}

x^{4} - 10 x^{2} + 9

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

x^{3} + x^{2} - 6 x + 3 = 0

x^{3} + 11 x^{2} + 34 x + 24 = 0

What are the solutions to the equation x^4+3x^3+3x^2+2x+1=0 ?
The solutions to the equation x^4+3x^3+3x^2+2x+1=0 are x=-1,x\approx-1.75487…
Find the zeros of x^4+3x^3+3x^2+2x+1=0
The zeros of x^4+3x^3+3x^2+2x+1=0 are x=-1,x\approx-1.75487…