What are the solutions to the equation x^5-6x+3=0 ?

The solutions to the equation x^5-6x+3=0 are x\approx 1.40164…,x\approx 0.50550…,x\approx-1.67093…

Find the zeros of x^5-6x+3=0

The zeros of x^5-6x+3=0 are x\approx 1.40164…,x\approx 0.50550…,x\approx-1.67093…

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x^{5} - 6 x + 3 = 0

x \approx 1.40164 \dots, x \approx 0.50550 \dots, x \approx - 1.67093 \dots

Solution steps

x^{5} - 6 x + 3 = 0

Find one solution for

x^{5} - 6 x + 3 = 0

using Newton-Raphson:

x \approx 1.40164 \dots

Apply long division:

\frac{x ^{5} - 6 x + 3}{x - 1.40164 \dots} = x^{4} + 1.40164 \dots x^{3} + 1.96459 \dots x^{2} + 2.75366 \dots x - 2.14034 \dots

x^{4} + 1.40164 \dots x^{3} + 1.96459 \dots x^{2} + 2.75366 \dots x - 2.14034 \dots \approx 0

Find one solution for

x^{4} + 1.40164 \dots x^{3} + 1.96459 \dots x^{2} + 2.75366 \dots x - 2.14034 \dots = 0

using Newton-Raphson:

x \approx 0.50550 \dots

Apply long division:

\frac{x ^{4} + 1.40164 \dots x ^{3} + 1.96459 \dots x ^{2} + 2.75366 \dots x - 2.14034 \dots}{x - 0.50550 \dots} = x^{3} + 1.90714 \dots x^{2} + 2.92866 \dots x + 4.23410 \dots

x^{3} + 1.90714 \dots x^{2} + 2.92866 \dots x + 4.23410 \dots \approx 0

Find one solution for

x^{3} + 1.90714 \dots x^{2} + 2.92866 \dots x + 4.23410 \dots = 0

using Newton-Raphson:

x \approx - 1.67093 \dots

Apply long division:

\frac{x ^{3} + 1.90714 \dots x ^{2} + 2.92866 \dots x + 4.23410 \dots}{x + 1.67093 \dots} = x^{2} + 0.23620 \dots x + 2.53397 \dots

x^{2} + 0.23620 \dots x + 2.53397 \dots \approx 0

Find one solution for

x^{2} + 0.23620 \dots x + 2.53397 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.40164 \dots, x \approx 0.50550 \dots, x \approx - 1.67093 \dots

x^{3} + 6 x^{2} = - x^{2} + 5 x + 2

(x - 5)^{3} + 12 = - 15

m^{4} + 2 m^{3} + 11 m^{2} + 2 m + 10 = 0

x^{2} (x^{2} - 3) = - 2

48 x + 10 x^{2} - 2 x^{3} = 0

What are the solutions to the equation x^5-6x+3=0 ?
The solutions to the equation x^5-6x+3=0 are x\approx 1.40164…,x\approx 0.50550…,x\approx-1.67093…
Find the zeros of x^5-6x+3=0
The zeros of x^5-6x+3=0 are x\approx 1.40164…,x\approx 0.50550…,x\approx-1.67093…