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

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

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

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

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

x = 1, x = - 2 + i, x = - 2 - i

Solution steps

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

Factor

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

(x - 1)^{3} (x^{2} + 4 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + 4 x + 5 = 0

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

x = 1, x = - 2 + i, x = - 2 - i

x^{3} - 10 x = 100

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

z^{4} + (- 4 + 2 i) z^{2} - 1 = 0

x^{3} + 3 x^{2} + 5 x + 2 = 0

x^{6} = 216

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