What are the solutions to the equation x^4+6x^3+11x^2+6x-48=0 ?

The solutions to the equation x^4+6x^3+11x^2+6x-48=0 are x=(sqrt(33)-3)/2 ,x=-(sqrt(33)+3)/2

Find the zeros of x^4+6x^3+11x^2+6x-48=0

The zeros of x^4+6x^3+11x^2+6x-48=0 are x=(sqrt(33)-3)/2 ,x=-(sqrt(33)+3)/2

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x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 48 = 0

x = \frac{33 - 3}{2}, x = - \frac{33 + 3}{2}

Decimal Notation

x = 1.37228 \dots, x = - 4.37228 \dots

Solution steps

x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 48 = 0

Find one solution for

x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 48 = 0

using Newton-Raphson:

x \approx 1.37228 \dots

Apply long division:

\frac{x ^{4} + 6 x ^{3} + 11 x ^{2} + 6 x - 48}{x - 1.37228 \dots} = x^{3} + 7.37228 \dots x^{2} + 21.11684 \dots x + 34.97825 \dots

x^{3} + 7.37228 \dots x^{2} + 21.11684 \dots x + 34.97825 \dots \approx 0

Find one solution for

x^{3} + 7.37228 \dots x^{2} + 21.11684 \dots x + 34.97825 \dots = 0

using Newton-Raphson:

x \approx - 4.37228 \dots

Apply long division:

\frac{x ^{3} + 7.37228 \dots x ^{2} + 21.11684 \dots x + 34.97825 \dots}{x + 4.37228 \dots} = x^{2} + 3 x + 8

x^{2} + 3 x + 8 \approx 0

Find one solution for

x^{2} + 3 x + 8 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx 1.37228 \dots : x = \frac{33 - 3}{2}

x \approx - 4.37228 \dots : x = - \frac{33 + 3}{2}

x = \frac{33 - 3}{2}, x = - \frac{33 + 3}{2}

The solutions are

x = \frac{33 - 3}{2}, x = - \frac{33 + 3}{2}

5 x^{3} - 40 = 0

x^{3} - 6 x^{2} + 16 = 0

a^{3} + 9 a^{2} - 58 a + 8 = 0

t^{3} - 9 t = 0

25 x^{4} + 16 = 41 x^{2}

What are the solutions to the equation x^4+6x^3+11x^2+6x-48=0 ?
The solutions to the equation x^4+6x^3+11x^2+6x-48=0 are x=(sqrt(33)-3)/2 ,x=-(sqrt(33)+3)/2
Find the zeros of x^4+6x^3+11x^2+6x-48=0
The zeros of x^4+6x^3+11x^2+6x-48=0 are x=(sqrt(33)-3)/2 ,x=-(sqrt(33)+3)/2