Question

Find the Q P. whose zeros are
1. 1/alpha,1/beta
2.1/alpha+1,1/beta+1​

Answer 1

Answer:

Consider the given polynomial

f(x)=x2−px+q

α and βare the zeros of given polynomial

 

We know that,

Sumofzeros=−cofficentofx2cofficentofx

α+β=1−(−p)

α+β=p

Productofzeros=cofficentofx2constant

α×β=1q

α×β=q

 

Then,

Part (1):-

α2+β2=(α+β)2−2αβ

α2+β2=p2−2q

 

Part (2):-

α1+β1=αβα+β

=qp