If α and β are the zeros of the quadratic polynomial 
, find a quadratic polynomial whose zeros are 
.
A quadratic equation when sum and product of its zeros is given by:
, where k is a constant
Sum of the roots = 
= 
= 
= 
Product of the roots = 
= 
= 
Sum of the zeros of new eqn = 
= 
⇒ 
= 
= 
= 
[Using (a + b)2 = a2 + b2 + 2ab]
⇒ 
= 
= 
Product of the zeros of new eqn = 
= 
⇒ 
= 
= 
= 
⇒ 
= 
= 
)
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and
, find a quadratic polynomial having α and
, find a quadratic polynomial whose zeros are 
, from a polynomial whose zeros are 
, find a polynomial whose roots are (i) 
(ii) 