What are the solutions to the equation x(x-3)(x-1)(x+2)=16 ?

The solutions to the equation x(x-3)(x-1)(x+2)=16 are x=(sqrt(33)+1)/2 ,x=-(sqrt(33)-1)/2

Find the zeros of x(x-3)(x-1)(x+2)=16

The zeros of x(x-3)(x-1)(x+2)=16 are x=(sqrt(33)+1)/2 ,x=-(sqrt(33)-1)/2

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x (x - 3) (x - 1) (x + 2) = 16

x = \frac{33 + 1}{2}, x = - \frac{33 - 1}{2}

Decimal

x = 3.37228 \dots, x = - 2.37228 \dots

Solution steps

x (x - 3) (x - 1) (x + 2) = 16

Expand

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

x^{4} - 2 x^{3} - 5 x^{2} + 6 x = 16

Move

16

to the left side

x^{4} - 2 x^{3} - 5 x^{2} + 6 x - 16 = 0

Find one solution for

x^{4} - 2 x^{3} - 5 x^{2} + 6 x - 16 = 0

using Newton-Raphson:

x \approx 3.37228 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} - 5 x ^{2} + 6 x - 16}{x - 3.37228 \dots} = x^{3} + 1.37228 \dots x^{2} - 0.37228 \dots x + 4.74456 \dots

x^{3} + 1.37228 \dots x^{2} - 0.37228 \dots x + 4.74456 \dots \approx 0

Find one solution for

x^{3} + 1.37228 \dots x^{2} - 0.37228 \dots x + 4.74456 \dots = 0

using Newton-Raphson:

x \approx - 2.37228 \dots

Apply long division:

\frac{x ^{3} + 1.37228 \dots x ^{2} - 0.37228 \dots x + 4.74456 \dots}{x + 2.37228 \dots} = x^{2} - x + 2

x^{2} - x + 2 \approx 0

Find one solution for

x^{2} - x + 2 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx 3.37228 \dots : x = \frac{33 + 1}{2}

x \approx - 2.37228 \dots : x = - \frac{33 - 1}{2}

x = \frac{33 + 1}{2}, x = - \frac{33 - 1}{2}

The solutions are

x = \frac{33 + 1}{2}, x = - \frac{33 - 1}{2}

(z + 3)^{4} = - 324

x, 3 (x - 3)^{4} = 15

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

x^{3} - 9 x - 4 = 0

x^{3} + x^{2} + 25 x + 25 = 0

What are the solutions to the equation x(x-3)(x-1)(x+2)=16 ?
The solutions to the equation x(x-3)(x-1)(x+2)=16 are x=(sqrt(33)+1)/2 ,x=-(sqrt(33)-1)/2
Find the zeros of x(x-3)(x-1)(x+2)=16
The zeros of x(x-3)(x-1)(x+2)=16 are x=(sqrt(33)+1)/2 ,x=-(sqrt(33)-1)/2