Question

Find the zeroes of the polynomial p(x)= x^3-2x^2-49x+98 if its two zeroes are equal in magnitude but opposite in sign.

Answer 1

Given 2 of its roots are equal but of opposite signs
Let α,β be equal roots 
such that β = -α

From this polynomial,
Sum of the roots ⇒ α+β+Δ  = -coefficient of x²/ coefficient of x³
                           ⇒ α-α+Δ = -(-2)/1
                                      Δ = 2   --------- One of the root (1)

Product of roots ⇒ αβΔ = -constant/coefficient of x³
                          ⇒ α(-α)Δ = -98/1
                          ⇒ -α²Δ = -98
                          ⇒ α²Δ = 98

From(1), Substituting Δ=2
                         ⇒ α²×2 = 98
                         ⇒ α² = 98/2
                         ⇒ α² = 49
                         ⇒ α = √49 = +-7
                         ⇒ α = +7 or -7              {where -7 = -α = β}

Therefore, the three roots of given polynomial x³-2x²-49x+98  α,β,Δ are +7,-7,2