Question

If and are zeroes of the quadratic polynomial 3x 2 – 4x + 1, find a quadratic polynomial whose zeroes are alpha/beta and beta/alpha​

Answer 1

Step-by-step explanation:

We have,

3x

2

−4x+1=0

α+β=

3

4

α.β=

3

1

β

2

α

2

+

α

2

β

2

=

αβ

(α+β)(α

2

+β

2

−α.β)

=

3

1

(α+β)((α+β)

2

−3αβ)

=4(

9

16

−1)=

9

4×7

=

9

28

β

α

2

×

α

β

2

=αβ=

3

1

Hence,

quadratic equation whose roots are

β

α

2 and

α

β

2 :

⇒x

2

−

9

28

x+

3

1

=0

9x

2

−28x+3=0