What are the solutions to the equation x^5-2x^4+1=0 ?

The solutions to the equation x^5-2x^4+1=0 are x=1,x\approx-0.77480…,x\approx 1.92756…

Find the zeros of x^5-2x^4+1=0

The zeros of x^5-2x^4+1=0 are x=1,x\approx-0.77480…,x\approx 1.92756…

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x^{5} - 2 x^{4} + 1 = 0

x = 1, x \approx - 0.77480 \dots, x \approx 1.92756 \dots

Solution steps

x^{5} - 2 x^{4} + 1 = 0

Factor

x^{5} - 2 x^{4} + 1 : (x - 1) (x^{4} - x^{3} - x^{2} - x - 1)

(x - 1) (x^{4} - x^{3} - x^{2} - x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{4} - x^{3} - x^{2} - x - 1 = 0 : x \approx - 0.77480 \dots, x \approx 1.92756 \dots

The solutions are

x = 1, x \approx - 0.77480 \dots, x \approx 1.92756 \dots

2 x^{3} = - 128

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

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

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

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

What are the solutions to the equation x^5-2x^4+1=0 ?
The solutions to the equation x^5-2x^4+1=0 are x=1,x\approx-0.77480…,x\approx 1.92756…
Find the zeros of x^5-2x^4+1=0
The zeros of x^5-2x^4+1=0 are x=1,x\approx-0.77480…,x\approx 1.92756…