Question

Given q² - pr < 0, p > 0, then the value of

Δ = |(p, q, px + qy), (q, r, qx + ry), (px + qy, qx + ry, 0)| is

(A) 0

(B) Positive

(C) Negative

(D) q² + pr 

Answer 1

Answer is (C) Negative

Applying R₃ → R₃ - xR₁ - yR₂ we get

⇒ (q² - pr)(px² + 2qxy + ry²) < 0

As q² - pr < 0 ⇒ Discriminant of quad < 0

⇒ (-ve) (+ve) < 0