What are the solutions to the equation 0=5x^4-6x+1 ?

The solutions to the equation 0=5x^4-6x+1 are x=1,x\approx 0.16731…

Find the zeros of 0=5x^4-6x+1

The zeros of 0=5x^4-6x+1 are x=1,x\approx 0.16731…

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0 = 5 x^{4} - 6 x + 1

x = 1, x \approx 0.16731 \dots

Solution steps

0 = 5 x^{4} - 6 x + 1

Switch sides

5 x^{4} - 6 x + 1 = 0

Factor

5 x^{4} - 6 x + 1 : (x - 1) (5 x^{3} + 5 x^{2} + 5 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

5 x^{3} + 5 x^{2} + 5 x - 1 = 0 : x \approx 0.16731 \dots

The solutions are

x = 1, x \approx 0.16731 \dots

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

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

3 = x^{3} + 2 x

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

6 x^{3} + 36 x - 12 = 0

What are the solutions to the equation 0=5x^4-6x+1 ?
The solutions to the equation 0=5x^4-6x+1 are x=1,x\approx 0.16731…
Find the zeros of 0=5x^4-6x+1
The zeros of 0=5x^4-6x+1 are x=1,x\approx 0.16731…