If the equations a1x2+b1x+c1=0  and a2x2+b2x+c2=0  posses a common root, then a1b1a2b2b1c1b2c2  is equal to

Let,  α  be the common root, then a1α2+b1α+c1=0,a2α2+b2α+c2=0 . Solving these equation we get, α2b1c2−b2c1=αa2c1−a1c2=1a1b2−a2b1  ⇒α2=b1c2−b2c1a1b2−a2b1,a2c1−a1c2a1b2−a2b1  ⇒(a2c1−a1c2a1b2−a2b1)2=b1c2−b2c1a1b2−a2b1  ⇒(a2c1−a1c2)2=(a1b2−a2b1)(b1c2−b2c1)  ⇒|a1     c1a2     c2|2=|b1     c1b2     c2||a1     b1a2     b2|