What are the solutions to the equation α^5-5α+4=0 ?

The solutions to the equation α^5-5α+4=0 are α=1,α\approx-1.65062…

Find the zeros of α^5-5α+4=0

The zeros of α^5-5α+4=0 are α=1,α\approx-1.65062…

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α^{5} - 5 α + 4 = 0

α = 1, α \approx - 1.65062 \dots

Solution steps

α^{5} - 5 α + 4 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

α - 1 = 0 or α^{3} + 2 α^{2} + 3 α + 4 = 0

Solve

α - 1 = 0 : α = 1

Solve

α^{3} + 2 α^{2} + 3 α + 4 = 0 : α \approx - 1.65062 \dots

The solutions are

α = 1, α \approx - 1.65062 \dots

x, y = x^{6}

x, (2 x + 3)^{4} = 3 y^{4}

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

x^{4} - 6 x^{3} + 14 x^{2} - 6 x + 13 = 0

y^{5} + 10 y^{4} + 100 y^{3} + 9.7 = 1

What are the solutions to the equation α^5-5α+4=0 ?
The solutions to the equation α^5-5α+4=0 are α=1,α\approx-1.65062…
Find the zeros of α^5-5α+4=0
The zeros of α^5-5α+4=0 are α=1,α\approx-1.65062…