What are the solutions to the equation roots x^4+3x^3-6x^2+12x-40 ?

The solutions to the equation roots x^4+3x^3-6x^2+12x-40 are x=2,x=-5,x=2i,x=-2i

Find the zeros of roots x^4+3x^3-6x^2+12x-40

The zeros of roots x^4+3x^3-6x^2+12x-40 are x=2,x=-5,x=2i,x=-2i

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roots

x^{4} + 3 x^{3} - 6 x^{2} + 12 x - 40

x = 2, x = - 5, x = 2 i, x = - 2 i

Solution steps

x^{4} + 3 x^{3} - 6 x^{2} + 12 x - 40

The roots are the intercepts with the x-axis

(y = 0)

x^{4} + 3 x^{3} - 6 x^{2} + 12 x - 40 = 0

Factor

x^{4} + 3 x^{3} - 6 x^{2} + 12 x - 40 : (x - 2) (x + 5) (x^{2} + 4)

(x - 2) (x + 5) (x^{2} + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x + 5 = 0 or x^{2} + 4 = 0

Solve

x - 2 = 0 : x = 2

Solve

x + 5 = 0 : x = - 5

Solve

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

The solutions are

x = 2, x = - 5, x = 2 i, x = - 2 i

125 x^{10} - 3 x^{7} = 0

x^{3} - 9 x^{2} + 28 x - 30 = 0

(- 2 x^{4} + 3 x^{2} + 8)^{2} = 0

x^{4} + 6 x^{2} - 91 = 0

x^{3} + x = 12

What are the solutions to the equation roots x^4+3x^3-6x^2+12x-40 ?
The solutions to the equation roots x^4+3x^3-6x^2+12x-40 are x=2,x=-5,x=2i,x=-2i
Find the zeros of roots x^4+3x^3-6x^2+12x-40
The zeros of roots x^4+3x^3-6x^2+12x-40 are x=2,x=-5,x=2i,x=-2i