Question

If r, s are the roots of the equation $x^2-px+q=0$, then what is the equation of the curve whose roots are $\left(\right[\frac{1}{r}]+s)$ and $\left(\right[\frac{1}{s}]+r)$?

• A. qx²+(p-q)x+(q²-1)=0
• B. (p-q)x²+pqx-(p+1)(q+1)=0
• C. qx²-p(q+1)x+(1+q)²=0
• D. qx²-p(q+1)x+(1+q)=0

Answer 1

The correct option is C qx²-p(q+1)x+(1+q)²=0

Put r=1 and s=1, then p=2 and q=1.

Roots of the curve’s equation = 2,2

Substitute values of p,q,r,s in options to check where 2,2 satisfy as roots. This happens only in option (c)