Question

If a and b are the zeroes of polynomial X²+bx+c=0 find the value of alfa /beta+ beta/alfa

Answer 1

Step-by-step explanation:

Sum of the roots of the given equation =α+β=

a

−b

...(1)

Product of the roots of the given equation =αβ=−

a

c

....(2)

β

α

2

+

α

β

2

=

αβ

α

3

+β

3

=

αβ

(α+β)(α

2

−αβ+β

2

)

=

αβ

(α+β)((α+β)

2

−2αβ−αβ)

=

αβ

(α+β)((α+β)

2

−3αβ)

....(3)

Substituting (1),(2) in (3), we get

β

α

2

+

α

β

2

=

−c/a

(−b/a)((−b/a)

2

−3(−c/a))

=

c

b

[

a

2

b

2

+

a

3c

]=

c

b

a

2

b

2

+3abc

=

a

2

c

b

3

+3abc