What are the solutions to the equation x^2-x^5+6=0 ?

The solutions to the equation x^2-x^5+6=0 are x\approx 1.52821…

Find the zeros of x^2-x^5+6=0

The zeros of x^2-x^5+6=0 are x\approx 1.52821…

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x^{2} - x^{5} + 6 = 0

x \approx 1.52821 \dots

Solution steps

x^{2} - x^{5} + 6 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- x^{5} + x^{2} + 6 = 0

Find one solution for

- x^{5} + x^{2} + 6 = 0

using Newton-Raphson:

x \approx 1.52821 \dots

Apply long division:

\frac{- x ^{5} + x ^{2} + 6}{x - 1.52821 \dots} = - x^{4} - 1.52821 \dots x^{3} - 2.33545 \dots x^{2} - 2.56909 \dots x - 3.92613 \dots

- x^{4} - 1.52821 \dots x^{3} - 2.33545 \dots x^{2} - 2.56909 \dots x - 3.92613 \dots \approx 0

Find one solution for

- x^{4} - 1.52821 \dots x^{3} - 2.33545 \dots x^{2} - 2.56909 \dots x - 3.92613 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.52821 \dots

5 x^{3} - 23 x^{2} + 29 x - 15 = 0

(x + 2)^{4} = 0

x^{4} - 4 x^{3} - 24 x^{2} + 20 x + 7 = 0

x = 9 x^{6} x 1 0^{22} x 1 0^{23}

x^{3} + 2 x - 4 = 0

What are the solutions to the equation x^2-x^5+6=0 ?
The solutions to the equation x^2-x^5+6=0 are x\approx 1.52821…
Find the zeros of x^2-x^5+6=0
The zeros of x^2-x^5+6=0 are x\approx 1.52821…