Question

The smallest number added to 680621

to make the sum a perfect square is ?
a. 4
b. 5
c. 6
d. 8​

Answer 1

Answer:

Step-by-step explanation:

Let α, β, Δ  be the roots of given polynomial x3-5x2-16x+80.

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 = -(-5)/1

                                     Δ = 5   --------- One of the root (1)

Product of roots ⇒ αβΔ = -constant/coefficient of x³

                         ⇒ α(-α)Δ = -80/1

                         ⇒ -α²Δ = -80

                         ⇒ α²Δ = 80

From(1), Substituting Δ=5

                        ⇒ α²×5 = 80

                        ⇒ α² = 80/5

                        ⇒ α² = 16

                        ⇒ α = √16 = +-4

                        ⇒ α = +4 or -4              {where -4 = -α = β}

the three roots of given polynomial x3-5x2-16x+80  α,β,Δ are 4,-4,5