Question

If α and β are the zeroes of the polynomial x

2 − x − 6, then find the values of:

(i) α
3 + β
3
(ii) α − β
(iii) α
2 + β
2

Answer 1

Answer:

Sum of the roots=α+β=

1

−3

=−3

Product of the roots=αβ=

1

6

=6

(i)

β

α

+

α

β

=

αβ

α

2

+β

2

=

αβ

(α+β)

2

−2αβ

=

6

(−3)

2

−2×6

=

6

9−12

=

6

−3

=

2

−1

(ii)α

2

+β

2

=(α+β)

2

−2αβ

=(−3)

2

−2×6

=9−12=−3