What are the solutions to the equation x^4-4x^3+7x^2-6x-18=0 ?

The solutions to the equation x^4-4x^3+7x^2-6x-18=0 are x=-1,x=3,x=1+sqrt(5)i,x=1-sqrt(5)i

Find the zeros of x^4-4x^3+7x^2-6x-18=0

The zeros of x^4-4x^3+7x^2-6x-18=0 are x=-1,x=3,x=1+sqrt(5)i,x=1-sqrt(5)i

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x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 = 0

x = - 1, x = 3, x = 1 + 5 i, x = 1 - 5 i

Solution steps

x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 = 0

Factor

x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 : (x + 1) (x - 3) (x^{2} - 2 x + 6)

(x + 1) (x - 3) (x^{2} - 2 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 3 = 0 or x^{2} - 2 x + 6 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 2 x + 6 = 0 : x = 1 + 5 i, x = 1 - 5 i

The solutions are

x = - 1, x = 3, x = 1 + 5 i, x = 1 - 5 i

x^{3} - 5 x^{2} = - 4 x

3 x^{6} - 14 x^{3} = 80

6 x^{2} x = 2

x^{8} = xx + 5

270 x - 3 x^{2} - 3 x^{3} = 0

What are the solutions to the equation x^4-4x^3+7x^2-6x-18=0 ?
The solutions to the equation x^4-4x^3+7x^2-6x-18=0 are x=-1,x=3,x=1+sqrt(5)i,x=1-sqrt(5)i
Find the zeros of x^4-4x^3+7x^2-6x-18=0
The zeros of x^4-4x^3+7x^2-6x-18=0 are x=-1,x=3,x=1+sqrt(5)i,x=1-sqrt(5)i