What are the solutions to the equation x^4-2x^3-10x^2+18x+9=0 ?

The solutions to the equation x^4-2x^3-10x^2+18x+9=0 are x=-3,x=3,x=1+sqrt(2),x=1-sqrt(2)

Find the zeros of x^4-2x^3-10x^2+18x+9=0

The zeros of x^4-2x^3-10x^2+18x+9=0 are x=-3,x=3,x=1+sqrt(2),x=1-sqrt(2)

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x^{4} - 2 x^{3} - 10 x^{2} + 18 x + 9 = 0

x = - 3, x = 3, x = 1 + 2, x = 1 - 2

Decimal Notation

x = - 3, x = 3, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

x^{4} - 2 x^{3} - 10 x^{2} + 18 x + 9 = 0

Factor

x^{4} - 2 x^{3} - 10 x^{2} + 18 x + 9 : (x + 3) (x - 3) (x^{2} - 2 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x - 3 = 0 or x^{2} - 2 x - 1 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 2 x - 1 = 0 : x = 1 + 2, x = 1 - 2

The solutions are

x = - 3, x = 3, x = 1 + 2, x = 1 - 2

4 (\frac{x ^{3}}{4})^{3} - 16 x = 0

x^{5} = - 243

0 = x^{5} - 2.2 x^{4} - 6.61 x^{3} + 8.602 x^{2}

x^{3} + 5 x^{2} - 36 x = 0

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

What are the solutions to the equation x^4-2x^3-10x^2+18x+9=0 ?
The solutions to the equation x^4-2x^3-10x^2+18x+9=0 are x=-3,x=3,x=1+sqrt(2),x=1-sqrt(2)
Find the zeros of x^4-2x^3-10x^2+18x+9=0
The zeros of x^4-2x^3-10x^2+18x+9=0 are x=-3,x=3,x=1+sqrt(2),x=1-sqrt(2)