What are the solutions to the equation x^3-11x^2+43x-65=0 ?

The solutions to the equation x^3-11x^2+43x-65=0 are x=5,x=3+2i,x=3-2i

Find the zeros of x^3-11x^2+43x-65=0

The zeros of x^3-11x^2+43x-65=0 are x=5,x=3+2i,x=3-2i

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x^{3} - 11 x^{2} + 43 x - 65 = 0

x = 5, x = 3 + 2 i, x = 3 - 2 i

Solution steps

x^{3} - 11 x^{2} + 43 x - 65 = 0

Factor

x^{3} - 11 x^{2} + 43 x - 65 : (x - 5) (x^{2} - 6 x + 13)

(x - 5) (x^{2} - 6 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x^{2} - 6 x + 13 = 0

Solve

x - 5 = 0 : x = 5

Solve

x^{2} - 6 x + 13 = 0 : x = 3 + 2 i, x = 3 - 2 i

The solutions are

x = 5, x = 3 + 2 i, x = 3 - 2 i

a^{5} + a^{2} = 36

x^{3} - 100 = 0

9 = x^{3} + 1

60 x^{4} + 120 x^{3} - 900 x^{2} = 0

x^{3} - 7 x^{2} + 24 x - 18 = 0

What are the solutions to the equation x^3-11x^2+43x-65=0 ?
The solutions to the equation x^3-11x^2+43x-65=0 are x=5,x=3+2i,x=3-2i
Find the zeros of x^3-11x^2+43x-65=0
The zeros of x^3-11x^2+43x-65=0 are x=5,x=3+2i,x=3-2i