What are the solutions to the equation x^4-x^3+3x^2-9x-54=0 ?

The solutions to the equation x^4-x^3+3x^2-9x-54=0 are x=-2,x=3,x=3i,x=-3i

Find the zeros of x^4-x^3+3x^2-9x-54=0

The zeros of x^4-x^3+3x^2-9x-54=0 are x=-2,x=3,x=3i,x=-3i

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x^{4} - x^{3} + 3 x^{2} - 9 x - 54 = 0

x = - 2, x = 3, x = 3 i, x = - 3 i

Solution steps

x^{4} - x^{3} + 3 x^{2} - 9 x - 54 = 0

Factor

x^{4} - x^{3} + 3 x^{2} - 9 x - 54 : (x + 2) (x - 3) (x^{2} + 9)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

x = - 2, x = 3, x = 3 i, x = - 3 i

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

2 x^{3} + 5 x^{2} + 32 x + 80 = 0

0 = x^{4}

t^{4} - 81 = 0

y^{4} = y^{2}

What are the solutions to the equation x^4-x^3+3x^2-9x-54=0 ?
The solutions to the equation x^4-x^3+3x^2-9x-54=0 are x=-2,x=3,x=3i,x=-3i
Find the zeros of x^4-x^3+3x^2-9x-54=0
The zeros of x^4-x^3+3x^2-9x-54=0 are x=-2,x=3,x=3i,x=-3i