If r and s are roots of `x^(2) + px + q = 0` , then what is the value of `(1//r^(2))+ ( 1//s^(2))` ?

Options

A. ` p^(2) - 4q`
B. ` (p^(2) - 4q)/2`
C. ` (p^(2)-4q)/q^(2)`
D. ` (p^(2) - 2q)/q^(2)`

Answer

D

Explanation

Since r and s are the roots of `x^(2) + px + q = 0 `
Then, `r+s= -p and rs = q `
Now, ` 1/r^(2)+1/s^(2)= r^(2) + (s^(2))/(rs)^(2)=((r+s)^(2)- 2rs)/(rs)^(2)`
`((-p)^(2)-2q)/q^(2)= (p^(2)-2q)/q^(2)`