If p and q are positive integers, then which one of the following equations has `p-sqrt(q)` as one of its roots ?

Options

A. `x^(2) - 2px - (p^(2)-q)=0`
B. ` x^(2) - 2px + (p^(2) - q)=0`
C. ` x^(2) + 2px - (p^(2)-q)=0`
D. ` x^(2) + 2px + (p^(2)-q)=0`

Answer

B

Explanation

If any equation has `p-sqrt(q)` as a root , then another root will be `p+sqrt(q).`
So, sum of roots ` = p-sqrt(q)+p+sqrt(q) = 2 p `
and product of roots `= (p-sqrt(q))(p+sqrt(q))=p^(2) - q`
Now, required equation is
`x^(2) - "(sum of roots ) x + ( product of roots ) "= 0`
`rArr x^(2) - 2 px + ( p^(2)-q) = 0 `