What are the solutions to the equation x^5-x^4-10x^3+10x^2-11x+11=0 ?

The solutions to the equation x^5-x^4-10x^3+10x^2-11x+11=0 are x=1,x=i,x=-i,x=-sqrt(11),x=sqrt(11)

Find the zeros of x^5-x^4-10x^3+10x^2-11x+11=0

The zeros of x^5-x^4-10x^3+10x^2-11x+11=0 are x=1,x=i,x=-i,x=-sqrt(11),x=sqrt(11)

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

x = 1, x = i, x = - i, x = - 11, x = 11

Solution steps

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

Factor

x^{5} - x^{4} - 10 x^{3} + 10 x^{2} - 11 x + 11 : (x - 1) (x^{2} + 1) (x + 11) (x - 11)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 1 = 0 : x = i, x = - i

Solve

x + 11 = 0 : x = - 11

Solve

x - 11 = 0 : x = 11

The solutions are

x = 1, x = i, x = - i, x = - 11, x = 11

4096 = x^{3}

12 \cdot 20 = x^{5}

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

26 = 16 \cdot (1 + x)^{4}

x^{6} - 2 x^{3} + 2

What are the solutions to the equation x^5-x^4-10x^3+10x^2-11x+11=0 ?
The solutions to the equation x^5-x^4-10x^3+10x^2-11x+11=0 are x=1,x=i,x=-i,x=-sqrt(11),x=sqrt(11)
Find the zeros of x^5-x^4-10x^3+10x^2-11x+11=0
The zeros of x^5-x^4-10x^3+10x^2-11x+11=0 are x=1,x=i,x=-i,x=-sqrt(11),x=sqrt(11)