What are the solutions to the equation x^5-3*x^2+x+1=0 ?

The solutions to the equation x^5-3*x^2+x+1=0 are x=1,x\approx-0.43015…

Find the zeros of x^5-3*x^2+x+1=0

The zeros of x^5-3*x^2+x+1=0 are x=1,x\approx-0.43015…

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

x = 1, x \approx - 0.43015 \dots

Solution steps

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

Factor

x^{5} - 3 x^{2} + x + 1 : (x - 1)^{2} (x^{3} + 2 x^{2} + 3 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{3} + 2 x^{2} + 3 x + 1 = 0 : x \approx - 0.43015 \dots

The solutions are

x = 1, x \approx - 0.43015 \dots

x^{3} + 3 x^{2} - 18 x - 40 = 0

y, 25 x^{4} - 625 y - 500 = 0

x^{4} + 2 x^{2} - x + 8

101 x^{100} + 51 x^{50} + 1 = 0

x^{4} - 4 x^{2} = x^{2} - 4

What are the solutions to the equation x^5-3*x^2+x+1=0 ?
The solutions to the equation x^5-3*x^2+x+1=0 are x=1,x\approx-0.43015…
Find the zeros of x^5-3*x^2+x+1=0
The zeros of x^5-3*x^2+x+1=0 are x=1,x\approx-0.43015…