What are the solutions to the equation x^4-3x^3-2x^2+10x-12=0 ?

The solutions to the equation x^4-3x^3-2x^2+10x-12=0 are x=-2,x=3,x=1+i,x=1-i

Find the zeros of x^4-3x^3-2x^2+10x-12=0

The zeros of x^4-3x^3-2x^2+10x-12=0 are x=-2,x=3,x=1+i,x=1-i

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x^{4} - 3 x^{3} - 2 x^{2} + 10 x - 12 = 0

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

Solution steps

x^{4} - 3 x^{3} - 2 x^{2} + 10 x - 12 = 0

Factor

x^{4} - 3 x^{3} - 2 x^{2} + 10 x - 12 : (x + 2) (x - 3) (x^{2} - 2 x + 2)

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

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

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

x^{4} - 256 = 0

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

y^{(4)} - 16 y = 0

x^{5} + x^{3} + x = 3

What are the solutions to the equation x^4-3x^3-2x^2+10x-12=0 ?
The solutions to the equation x^4-3x^3-2x^2+10x-12=0 are x=-2,x=3,x=1+i,x=1-i
Find the zeros of x^4-3x^3-2x^2+10x-12=0
The zeros of x^4-3x^3-2x^2+10x-12=0 are x=-2,x=3,x=1+i,x=1-i