The quadratic equations x2−6x+a=0 and x2−cx+6=0 have one root α in common. The other roots of the first and second equations are integers in the ratio 4: 3. Then equation x2−3x−4=0 has

Let equation x2−6x+a=0 have roots α and βAlso, let equation x2−cx+6=0 have roots α and γGiven βγ=43 ⇒αβαγ=43 ⇒a6=43 ⇒a=8First equation is x2−6x+8=0⇒ (x−2)(x−4)=0⇒ x=2,4If β=4, then γ=3β4=3If β=2, then γ=3β4=32, which is not an integer.Now, x2−3x−4=0⇒ (x−4)(x+1)=0⇒ x=−1,4Clearly, one root is less than 2 and other is more than2