(Q7)Find the quadratic polynomial, whose sum and product of the zeros are -3 and 2 respectively.

Answer:

Let the quadratic polynomial be ax2+bx+c, and its zeros be α and β we have

α+β=
-b
a
αβ=
c
a

If we take a = 1 then b = 3 and c = 2

So, one quadratic polynomial which fits the given conditions is x2 + 3x + 2

similarly, we can take 'a' to be any real number.Let us say it is k.this gives
-b
k
 = - or b=k and
c
k
= or c= k

substituting the values of a,b and c we get the polynomial as kx2+kx+k