What are the solutions to the equation x^3-5x^2-2x+6=0 ?

The solutions to the equation x^3-5x^2-2x+6=0 are x=1,x=2+sqrt(10),x=2-sqrt(10)

Find the zeros of x^3-5x^2-2x+6=0

The zeros of x^3-5x^2-2x+6=0 are x=1,x=2+sqrt(10),x=2-sqrt(10)

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

x = 1, x = 2 + 10, x = 2 - 10

Decimal

x = 1, x = 5.16227 \dots, x = - 1.16227 \dots

Solution steps

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

Factor

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

(x - 1) (x^{2} - 4 x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 4 x - 6 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 4 x - 6 = 0 : x = 2 + 10, x = 2 - 10

The solutions are

x = 1, x = 2 + 10, x = 2 - 10

x^{4} + 2 x^{3} + 2 x^{2} = 0

x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} + 11 x + 10 = 0

x^{3} = x^{2} + 20 x

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

16 x^{3} - 4 x^{2} - 20 x + 5

What are the solutions to the equation x^3-5x^2-2x+6=0 ?
The solutions to the equation x^3-5x^2-2x+6=0 are x=1,x=2+sqrt(10),x=2-sqrt(10)
Find the zeros of x^3-5x^2-2x+6=0
The zeros of x^3-5x^2-2x+6=0 are x=1,x=2+sqrt(10),x=2-sqrt(10)