What are the solutions to the equation x^4-3x^3+6x^2+2x-60=0 ?

The solutions to the equation x^4-3x^3+6x^2+2x-60=0 are x=-2,x=3,x=1+3i,x=1-3i

Find the zeros of x^4-3x^3+6x^2+2x-60=0

The zeros of x^4-3x^3+6x^2+2x-60=0 are x=-2,x=3,x=1+3i,x=1-3i

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x^{4} - 3 x^{3} + 6 x^{2} + 2 x - 60 = 0

x = - 2, x = 3, x = 1 + 3 i, x = 1 - 3 i

Solution steps

x^{4} - 3 x^{3} + 6 x^{2} + 2 x - 60 = 0

Factor

x^{4} - 3 x^{3} + 6 x^{2} + 2 x - 60 : (x + 2) (x - 3) (x^{2} - 2 x + 10)

(x + 2) (x - 3) (x^{2} - 2 x + 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x - 3 = 0 or x^{2} - 2 x + 10 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 2 x + 10 = 0 : x = 1 + 3 i, x = 1 - 3 i

The solutions are

x = - 2, x = 3, x = 1 + 3 i, x = 1 - 3 i

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

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

2 x^{3} + 3 x^{2} + 32 x + 48 = 0

8 x^{3} - 72 x = 0

(3 - x)^{3} = 125

What are the solutions to the equation x^4-3x^3+6x^2+2x-60=0 ?
The solutions to the equation x^4-3x^3+6x^2+2x-60=0 are x=-2,x=3,x=1+3i,x=1-3i
Find the zeros of x^4-3x^3+6x^2+2x-60=0
The zeros of x^4-3x^3+6x^2+2x-60=0 are x=-2,x=3,x=1+3i,x=1-3i