Book: RD Sharma - Mathematics
Chapter: 2. Polynomials
Subject: Maths - Class 10th
Q. No. 19 of Exercise 2.1
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19
If α and β are the zeros of the quadratic polynomial 
, find a polynomial whose roots are (i) 
(ii) 
.
(i)
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 = 
= 
Product of the zeros of new eqn =
=
(ii) 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 = 
= 
= 
= 
= 
Product of the zeros of new eqn =
= 
= 
= 
= 
Therefore eqn is: 
= 
= 
= 
= 0
, find the value of 
, find the value of 
.
, find the value of
, find the value of 
, find the value of 
, find the value of 
, find the value of
, find the value of 
is negative of the other, find the value of k.
is equal to their product, find the value of k.
is equal to 144, find the value of p.
, prove that 
, show that 
and
, find a quadratic polynomial having α and
, find a quadratic polynomial whose zeros are 
, find a quadratic polynomial whose zeros are 
, from a polynomial whose zeros are 
, then evaluate:
(ii) 
(vi) 
