Question

We have the equation: `x^3-28x+m=0;` with `m inRR`.For which values o `m` one root of the equation is double the other root?

Answer 1

`m = pm 48`

Explanation:

Considering the roots as `r_1,r_2,r_3` we know that `r_3 = 2r_2` we have

`x^3 - 28 x + m - (x - r_1) (x - r_2) (x - 2 r_2) = 0`

Equating the coefficients we have the conditions:

`{(m + 2 r_1 r_2^2=0), (28 + 3 r_1 r_2 + 2 r_2^2=0), (r_1 + 3 r_2=0):}`

Now solving for `m, r_1,r_2` we have

`r_1=6,r_2=-2,m=-48` or
`r_1=-6,r_2=2,m=48`

So we have two outcomes `m = pm 48`