Question

If p, q, r, s are rational numbers & roots of f(x) = 0 are eccentricities of a parabola & a rectangular hyperbola where

f(x) = px³ + qx² + rx + s, then p + q + r + s =

• A. p
• B. – p
• C. 2p
• D. 0

Answer 1

Answer: (D)

0

Answer 2

Roots of f(x) = 0 are 1,$\sqrt{2}$ & $- \sqrt{2}$

(\ irrational root occur in pair)

\ f(x) = p (x – 1) $(x - \sqrt{2})(x + \sqrt{2})$

= p (x³ – x² – 2x + 2)

\ p + q + r + s = p – p – 2p + 2p = 0