What are the solutions to the equation x^3-21x^2+111x-11=0 ?

The solutions to the equation x^3-21x^2+111x-11=0 are x=11,x=5+2sqrt(6),x=5-2sqrt(6)

Find the zeros of x^3-21x^2+111x-11=0

The zeros of x^3-21x^2+111x-11=0 are x=11,x=5+2sqrt(6),x=5-2sqrt(6)

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x^{3} - 21 x^{2} + 111 x - 11 = 0

x = 11, x = 5 + 26, x = 5 - 26

Decimal Notation

x = 11, x = 9.89897 \dots, x = 0.10102 \dots

Solution steps

x^{3} - 21 x^{2} + 111 x - 11 = 0

Factor

x^{3} - 21 x^{2} + 111 x - 11 : (x - 11) (x^{2} - 10 x + 1)

(x - 11) (x^{2} - 10 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 11 = 0 or x^{2} - 10 x + 1 = 0

Solve

x - 11 = 0 : x = 11

Solve

x^{2} - 10 x + 1 = 0 : x = 5 + 26, x = 5 - 26

The solutions are

x = 11, x = 5 + 26, x = 5 - 26

x^{4} - 18 x^{2} = 18 x^{2}

x (x + 3) (x + 3) = 0

x^{3} + 4 x^{2} + x - 26 = 0

9 x^{3} - 25 x = 0

(1 + j)^{4} = 1.1

What are the solutions to the equation x^3-21x^2+111x-11=0 ?
The solutions to the equation x^3-21x^2+111x-11=0 are x=11,x=5+2sqrt(6),x=5-2sqrt(6)
Find the zeros of x^3-21x^2+111x-11=0
The zeros of x^3-21x^2+111x-11=0 are x=11,x=5+2sqrt(6),x=5-2sqrt(6)