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

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

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

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

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

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

Solution steps

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

Switch sides

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

t^{3} - t^{2} - t + 1 = 0

(k^{3} - 1)^{2} = 0

a^{8} = 3

y^{4} - 12 y^{2} + 32 = 0

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

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