Question

find the zeros of the polynomial f(x)x³+4x²-9x-36,if 2 of its zeroes are equal in magnitude but opposite in sign

Answer 1

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

Given:

α = –b

Now

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

and product of roots = αbγ = α(–α)γ

= – α2 γ = – 75

⇒ 3α2 = 75

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