Question

If every pair from among the equation $x^2 + px + qr = 0$, $x^2 + qx + rp = 0$ and $x^2 + rx + pq = 0$ has a common root, then the product of three common roots is.

• A. $pqr$
• B. $2pqr$
• C. $p^2 q^2 r^2$
• D. none of these

Answer 1

Answer: (A)

$pqr$

Answer 2

$\alpha \beta = qr, \beta \gamma = rp, \gamma \alpha = pq$ $\therefore \, (\alpha \beta ) (\beta \gamma ) (\gamma \alpha ) = (qr) (rp) (pq)$ $\Rightarrow \, (\alpha \beta \gamma)^2 = (pqr)^2$ $\Rightarrow \, \alpha \beta = pqr$