Roots of cubed: x-1=0, x=1; x^2-1=0, x=+1,-1; x^3-1=0, x=?

[matthew042]

Degree n equation has n roots.

Degree 1 x-1=0 x=1

Degree 2 x(squared) -1 = 0 x= +1, -1

Degree 3 x(cubed) -1 = 0 x= 1, ?, ?

Please reply with answer and how to get that.

 

[Deleted member 4993]

Re: Roots of cubed

Degree n equation has n roots.

Degree 1 x-1=0 x=1

Degree 2 x(squared) -1 = 0 x= +1, -1

Degree 3 x(cubed) -1[sup:24jnvdt1]3[/sup:24jnvdt1] = 0 x= 1, ?, ?

use

a[sup:24jnvdt1]3[/sup:24jnvdt1] - b[sup:24jnvdt1]3[/sup:24jnvdt1] = (a - b)(a[sup:24jnvdt1]2[/sup:24jnvdt1] + ab + b[sup:24jnvdt1]2[/sup:24jnvdt1])

 

[stapel]

Please reply with answer and how to get that.

Have you studied complex numbers yet?

If so, then use the difference-of-cubes formula, provided in the previous reply, to factor out the one linear factor (which gives you the zero that you have already noted).

Then apply the Quadratic Formula to the other factor to obtain the two complex-valued zeroes. :wink: