What are the solutions to the equation -x^3+8x^2-13x+2=0 ?

The solutions to the equation -x^3+8x^2-13x+2=0 are x=2,x=3+2sqrt(2),x=3-2sqrt(2)

Find the zeros of -x^3+8x^2-13x+2=0

The zeros of -x^3+8x^2-13x+2=0 are x=2,x=3+2sqrt(2),x=3-2sqrt(2)

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- x^{3} + 8 x^{2} - 13 x + 2 = 0

x = 2, x = 3 + 22, x = 3 - 22

Decimal Notation

x = 2, x = 5.82842 \dots, x = 0.17157 \dots

Solution steps

- x^{3} + 8 x^{2} - 13 x + 2 = 0

Factor

- x^{3} + 8 x^{2} - 13 x + 2 : - (x - 2) (x^{2} - 6 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 6 x + 1 = 0 : x = 3 + 22, x = 3 - 22

The solutions are

x = 2, x = 3 + 22, x = 3 - 22

r^{4} - r + 1 = 0

x^{3} - 5 x^{2} - 8 x = 12

z^{4} = - 2 - 23

10 x (x^{2} - 4)^{4} = 0

6 x^{3} + 6 x^{2} - 7 x + 2 = 0

What are the solutions to the equation -x^3+8x^2-13x+2=0 ?
The solutions to the equation -x^3+8x^2-13x+2=0 are x=2,x=3+2sqrt(2),x=3-2sqrt(2)
Find the zeros of -x^3+8x^2-13x+2=0
The zeros of -x^3+8x^2-13x+2=0 are x=2,x=3+2sqrt(2),x=3-2sqrt(2)