If `a(p+q)^2+2b p q+c=0a b da(p+r)^2+2b p r+c=0(a!=0)` , then `q r=p^2` b. `q r=p^2+c/a` c. `q r=p^2` d. none of these

Options

A. `qr = p^(2) + (c)/(a)`
B. `qr = p^(2)`
C. `(q + r)/(a + b) = -(2p)/(a)`
D. `(q + r)/(a + b) = -(p)/(a)`

Answer

A, C

Explanation

`q` and `r` are the roots of the equation
`a(p + x)^(2) + 2bpx + c = 0`
`ax^(2) + 2(a + b)px + ap^(2) + c = 0`
`rArr` Product of roots is `qr = (ap^(2) + c)/(a) rArr qr = p^(2) + (c)/(a)`
Sum of roots is `q + r = -(2p(a + b))/(a)`