What are the solutions to the equation x^3-11x^2+35x-33=0 ?

The solutions to the equation x^3-11x^2+35x-33=0 are x=3,x=4+sqrt(5),x=4-sqrt(5)

Find the zeros of x^3-11x^2+35x-33=0

The zeros of x^3-11x^2+35x-33=0 are x=3,x=4+sqrt(5),x=4-sqrt(5)

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x^{3} - 11 x^{2} + 35 x - 33 = 0

x = 3, x = 4 + 5, x = 4 - 5

Decimal Notation

x = 3, x = 6.23606 \dots, x = 1.76393 \dots

Solution steps

x^{3} - 11 x^{2} + 35 x - 33 = 0

Factor

x^{3} - 11 x^{2} + 35 x - 33 : (x - 3) (x^{2} - 8 x + 11)

(x - 3) (x^{2} - 8 x + 11) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} - 8 x + 11 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 8 x + 11 = 0 : x = 4 + 5, x = 4 - 5

The solutions are

x = 3, x = 4 + 5, x = 4 - 5

x^{2} = x (12100 x^{2} - 220 x + 1)

x^{3} + 10 x - 5 = 0

0 = x^{3} - 10 x^{2} + 24 x

\frac{125}{64} = 125 r^{6}

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

What are the solutions to the equation x^3-11x^2+35x-33=0 ?
The solutions to the equation x^3-11x^2+35x-33=0 are x=3,x=4+sqrt(5),x=4-sqrt(5)
Find the zeros of x^3-11x^2+35x-33=0
The zeros of x^3-11x^2+35x-33=0 are x=3,x=4+sqrt(5),x=4-sqrt(5)