There is only one real value of 'a' for which the quadratic equation `ax^2+(a+3)x+a-3=0` has two positive integral solutions. The product of these two solutions is

Options

A. 9
B. 8
C. 6
D. 12

Answer

B

Explanation

Sum of the roots `=-((a+3))/a=-I^(+)`[let]
`:.a=(-3/(I^(+)+1))`..i
Product of the roots `=alpha beta=(a-3)/a=I^(+)+2`….ii
and `D=(a+3)^(2)-4a(a+3)`
`=9/((I^(+)+1)^(2)){(I^(+)-2)^(2)-12}` [from Eq. (i)]
D must be perfect square then `I^(+)=6`
From Eq. (ii)
Product of the roots `=I^(+)+2=6+2-8`