Question

if every pair of the equations x^2 + px+qr=0 , x^2 +qx+rp=0 , x^2 +rx + pq =0 have a non - zero common root , then sum of three common roots is

Answer 1

Answer: pqr

Step-by-step explanation:

Let a be the common root of x² + px + qr =0 and

x² + qx + rp = 0 (1)

Let b be the common root of x² + px + qr =0 and x² + rx + pq = 0

Let c be the common root of x² + qx + pr =0 and x² + rx + pq = 0

From (1),

a² + pa + qr =0 and a² + qa + rp = 0

⇒pa + qr = qa + rp

⇒a(p-q) = r(p-q)

⇒a = r

Similarly we can prove that b=q and c =p

So the product of the common roots is abc=pqr