Question

if x1, x2... x2019 are the roots of x^2019+1=0 find the product (1+x1)(1+x2)(1+x2019)​

Answer 1

Answer:

x

1

, x

2

and x

3

are the roots of equation

x

3

−2px

2

+3qx−1=0

⇒ x

1

+x

2

+x

3

=3p

x

1

x

2

+x

2

+x

3

+x

3

x

1

=3q

x

1

x

2

x

3

=1

Now, centroid of triangle with vertices

(m

1

,n

1

) (m

2

,n

2

) (m

3

,n

3

) is

(

3

m

1

+m

2

+m

3

,

3

n

1

+n

2

+n

3

)

∴ vertices of centroid

(

3

x

1

+x

2

+x

3

,

3

1/x

1

+1/x

2

+1/x

3

)

⇒ (3 p/3,

3x

1

x

2

x

3

x

1

x

2

+x

2

x

3

+x

1

x

3

)

⇒ [P,

3(1)

3q

]

(p, q)

I think this method