Condition for a common root (c1a2−c2a1)2=(b1c2−b2c1)(a1b2−a2b1) ⇒(3c−(−5c))2=(35c−3c)(1−(−7)) ⇒64c2=32c×8 ⇒c2=4c ∴c=4[∵c≠0] Now, the given expression becomes x2−3x+4 'It discriminant D=9−16=−7<0 Coefficient of x2=1>0 Hence, the given expression is positive ∀x∈R .