Question

If p and q are zeroes of quadratic polynomial (x^2)-6x+a , find the value of a if 3p+2q=20

Answer 1

If p and q are zeroes of quadratic polynomial (x^2)-6x+a , then
p+q = 6 and pq = a

Now, 3p +2q = 20
or, 3p +2(6-p) = 20
or, 3p+12-2p =20
or, p+12 =20
or, p = 20-12 =8
then q = 6-p = 6-8 =-2
Hence, a =pq = 8(-2) = -16 Ans.