What are the solutions to the equation x^4-5x^3-5x^2+23x+10=0 ?

The solutions to the equation x^4-5x^3-5x^2+23x+10=0 are x=-2,x=5,x=1+sqrt(2),x=1-sqrt(2)

Find the zeros of x^4-5x^3-5x^2+23x+10=0

The zeros of x^4-5x^3-5x^2+23x+10=0 are x=-2,x=5,x=1+sqrt(2),x=1-sqrt(2)

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x^{4} - 5 x^{3} - 5 x^{2} + 23 x + 10 = 0

x = - 2, x = 5, x = 1 + 2, x = 1 - 2

Decimal Notation

x = - 2, x = 5, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

x^{4} - 5 x^{3} - 5 x^{2} + 23 x + 10 = 0

Factor

x^{4} - 5 x^{3} - 5 x^{2} + 23 x + 10 : (x + 2) (x - 5) (x^{2} - 2 x - 1)

(x + 2) (x - 5) (x^{2} - 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x - 5 = 0 or x^{2} - 2 x - 1 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 5 = 0 : x = 5

Solve

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

The solutions are

x = - 2, x = 5, x = 1 + 2, x = 1 - 2

2300000 = 2000000 \cdot (1 + x)^{6}

13 + x^{3} = 7 x^{2} + 13

x^{30} = 3

x^{4} + x^{3} = x^{4} + x^{2} + 6 x

(x) = (5 x^{2} - 3) (x^{2} + x + 4)

What are the solutions to the equation x^4-5x^3-5x^2+23x+10=0 ?
The solutions to the equation x^4-5x^3-5x^2+23x+10=0 are x=-2,x=5,x=1+sqrt(2),x=1-sqrt(2)
Find the zeros of x^4-5x^3-5x^2+23x+10=0
The zeros of x^4-5x^3-5x^2+23x+10=0 are x=-2,x=5,x=1+sqrt(2),x=1-sqrt(2)