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 = 0.41421 \dots, x = - 2.41421 \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

x^{4} = (x - 20)^{2}

+ 4 x^{8} - 9 = 2

x^{6} - 7 x^{2} - 8 = 0

3 x^{5} - 5 x^{4} + 2 x^{3} - x^{2} + 4 x - 1 = 0

x^{4} - 2.3 x^{3} + 4 = 4

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)