find zeroes of polynomial x^3-3x^2-25x+75 if its two zeroes are equal; in magnitude but opposite in direction

Let α, β, and γ be the zeroes of x³ – 3x² – 25x + 75

Given:

α = –β

Now

Sum of roots = α + β + γ = α – α + γ = γ =3

and product of roots = αβγ = α(–α)γ

= – α² γ = – 75

⇒ 3α² = 75

So, the required zeroes are 3, 5 and – 5