Question

.........................​

Answer 1

Answer :-

__________________________

p ( x ) = 3x² - 4x + 1 , Then , a = 3 , b = -4 , c = 1

Now , if the zeros of the polynomial are α and β

Then , αβ = c / a = 1 / 3

And , α + β = - b / a = 4 / 3

Therefore ,

α² / β + β² / α

= α³ + β³ / αβ

= ( α + β )³ - 3αβ ( α + β ) / αβ

= [ ( 4 / 3 )³ - 3 × 1 / 3 × 4 / 3 ] / [ 1 / 3 ]

= [ 64 / 27 - 4 / 3 ] / [ 1 / 3 ]

= [ 64 - 36 / 27 ] / [ 1 / 3 ]

= 28 / 27 × 3

= 28 / 9

And ,

α² / β × β² / α

= αβ

= 1 / 3


•°• The polynomial will be ,

p ( x ) = x² - ( α² / β + β² / α )x + ( α² / β × β² / α )

= x² - 28x / 9 + 1 / 3 [ • Required answer ]

________________

Thanks!