Question

if alpha and beta are the zeroes of the quadratic polynomial 5x²-6x+1 ,find a quadratic polynomial whose zeroes are alpha/beta² and beta /alpha²​

Answer 1

Answer:

(x)=3x

2

−5x−2

α+β=

3

5

,αβ=

3

−2

Given,

β

α

2

+

α

β

2

=

αβ

α

3

+β

3

=

αβ

(α+β)(α

2

+β

2

−αβ)

=

αβ

(α+β)∫(α+β)

2

−3αβ

=

−2/3

(

3

5

)(

9

25

+2.)

=

2

−5

(

9

43

)=

16

−215