If `a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0)` , then which one is correct? a) `q r=p^2` b) `q r=p^2+c/a` c) none of these d) either a) or b)

Options

A. `qr = p^(2)`
B. `qr = p^(2) + c/a`
C. `qr = -p^(2)`
D. none of these

Answer

2

Explanation

Given, `a(p + q)^(2) + 2bpq + c = 0 and a(p + r)^(2) + 2bpr + c = 0`
`rArr` q and r satisfy the equation `a(p + x)^(2) + 2bpx + c = 0`
`rArr` q and r are the roots of `ax^(2) + 2(ap + bp)x + c + ap^(2) = 0`
`rArr` qr = Product of roots `= (c + ap^(2))/(a) = p^(2) + c/a`