Question

Please answer the 41st question. It will be really appreciated

Answer 1

Answer:

the answer is in the pic

Answer 2

Answer:

Required polynomial is x^2 - $\dfrac{16}{3}x + \dfrac{16}{3}$,

Step-by-step explanation:

Note : Alpha is written as A and beta is written as B.

Given, A and B are the zeroes of polynomial x^2 + 4x + 3.

= > x^2 + 4x + 3

= > x^2 + ( 3 + 1 )x + 3

= > x^2 + 3x + x + 3

= > x( x + 3 ) + ( x + 3 )

= > ( x + 3 )( x + 1 )

Zeroes are : ( - 3 ) and ( - 1 )

So, A = - 3 or - 1 or B = - 1 or - 3 { depends on value taken for A }

Here, we have to find out the polynomial whose zeroes are : 1 + A / B and 1 + B / A.

= > We have to equation whose zeroes are : ( B + A ) / B and ( A + B ) / A = > ( - 3 - 1 ) / - 1 and ( - 1 - 3 ) / - 3 = > 4 and 4 / 3.

Product of zeroes :

= > 4 × ( 4 / 3 )

= > 16 / 3

Sum of zeroes :

= > 4 + 4 / 3

= > ( 12 + 4 ) / 3

= > 16 / 3

Therefore,

= > Required polynomial : k[ x^2 - ( sum of zeroes )x + ( product of zeroes ) ]

= > Required polynomial : k[ x^2 - 16x / 3 + 16 / 3 ]

Hence the required polynomial is x^2 - $\dfrac{16}{3}x + \dfrac{16}{3}$, if k is 1.