What are the solutions to the equation x^3-6x^2+15x-14=0 ?

The solutions to the equation x^3-6x^2+15x-14=0 are x=2,x=2+sqrt(3)i,x=2-sqrt(3)i

Find the zeros of x^3-6x^2+15x-14=0

The zeros of x^3-6x^2+15x-14=0 are x=2,x=2+sqrt(3)i,x=2-sqrt(3)i

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x^{3} - 6 x^{2} + 15 x - 14 = 0

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

Solution steps

x^{3} - 6 x^{2} + 15 x - 14 = 0

Factor

x^{3} - 6 x^{2} + 15 x - 14 : (x - 2) (x^{2} - 4 x + 7)

(x - 2) (x^{2} - 4 x + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} - 4 x + 7 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 4 x + 7 = 0 : x = 2 + 3 i, x = 2 - 3 i

The solutions are

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

x^{3} = 1 + x + x^{2}

2 x^{3} - 2 x^{2} - 24 x = 0

y^{2} y^{2} + y + 32 = (y - 4)^{2}

3 x^{3} - 5 x^{2} + 6 x = 0

- x^{3} - 5 x^{2} + 6 x + 32 = 0

What are the solutions to the equation x^3-6x^2+15x-14=0 ?
The solutions to the equation x^3-6x^2+15x-14=0 are x=2,x=2+sqrt(3)i,x=2-sqrt(3)i
Find the zeros of x^3-6x^2+15x-14=0
The zeros of x^3-6x^2+15x-14=0 are x=2,x=2+sqrt(3)i,x=2-sqrt(3)i