What are the solutions to the equation x^4-2x^3+6x^2-18x-27=0 ?

The solutions to the equation x^4-2x^3+6x^2-18x-27=0 are x=-1,x=3,x=3i,x=-3i

Find the zeros of x^4-2x^3+6x^2-18x-27=0

The zeros of x^4-2x^3+6x^2-18x-27=0 are x=-1,x=3,x=3i,x=-3i

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x^{4} - 2 x^{3} + 6 x^{2} - 18 x - 27 = 0

x = - 1, x = 3, x = 3 i, x = - 3 i

Solution steps

x^{4} - 2 x^{3} + 6 x^{2} - 18 x - 27 = 0

Factor

x^{4} - 2 x^{3} + 6 x^{2} - 18 x - 27 : (x + 1) (x - 3) (x^{2} + 9)

(x + 1) (x - 3) (x^{2} + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 3 = 0 or x^{2} + 9 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 9 = 0 : x = 3 i, x = - 3 i

The solutions are

x = - 1, x = 3, x = 3 i, x = - 3 i

r^{3} + r^{2} - r - 1 = 0

x^{4} - x^{2} + \frac{1}{4} = 0

x^{3} - 12 x + 11 = 0

7 x^{3} - x^{2} - 7 x + 1

4 s^{3} + 15 s^{2} + 18 s + 5 = 0

What are the solutions to the equation x^4-2x^3+6x^2-18x-27=0 ?
The solutions to the equation x^4-2x^3+6x^2-18x-27=0 are x=-1,x=3,x=3i,x=-3i
Find the zeros of x^4-2x^3+6x^2-18x-27=0
The zeros of x^4-2x^3+6x^2-18x-27=0 are x=-1,x=3,x=3i,x=-3i