What are the solutions to the equation x^3-13x^2+23x-11=0 ?

The solutions to the equation x^3-13x^2+23x-11=0 are x=1,x=11

Find the zeros of x^3-13x^2+23x-11=0

The zeros of x^3-13x^2+23x-11=0 are x=1,x=11

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x^{3} - 13 x^{2} + 23 x - 11 = 0

x = 1, x = 11

Solution steps

x^{3} - 13 x^{2} + 23 x - 11 = 0

Factor

x^{3} - 13 x^{2} + 23 x - 11 : (x - 1)^{2} (x - 11)

(x - 1)^{2} (x - 11) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x - 11 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 11 = 0 : x = 11

The solutions are

x = 1, x = 11

x^{3} + 2 x^{2} - 16 x - 32

x^{4} - 2 x^{3} + x^{2} + 12 x + 8 = 0

(x + 4) (x^{2} - x + 3) = 0

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

x^{4} - x^{3} - 27 x + 27

What are the solutions to the equation x^3-13x^2+23x-11=0 ?
The solutions to the equation x^3-13x^2+23x-11=0 are x=1,x=11
Find the zeros of x^3-13x^2+23x-11=0
The zeros of x^3-13x^2+23x-11=0 are x=1,x=11