Question

If α and β are the zeros of the polynomial 2x²−x-1, find the value of 1/ α²+1/β²​

Answer 1

Answer:

2x

2

−4x+5

α+β=

a

−b

=

2

−(−4)

=

2

4

=2

αβ=

a

c

=

2

5

(α

2

+β

2

)=(α+β)

2

−2αβ

=4−5=−1

α

1

+

β

1

=

αβ

α+β

=

2

5

2

=

5

4

(α−β)

2

=(α

2

+β

2

)−2αβ

=−1−2(

2

5

)=−1−5

=−6

(α

3

+β

3

)=(α+β)(α

2

+β

2

−αβ)

=(2)(−1

2

−5

)

=2(

2

−7

)=−7