The quadratic equations x^2-6 x+a=0 and x^2-c x+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4: 3 . Then the common root is

Step-by-step solution

Let and 4 be roots of x^2-6 x+a=0 and , 3 be the roots of x^2-c x+6=0 , then +4 =6 and 4 =a +3 =c and 3 =6 . We get =2 a=8 So the first equation is x^2-6 x+8=0 x=2,4 If =2 and 4 =4 then 3 =3 If =4 and 4 =2 , then 3 =3 / 2 (non-integer) common root is x=2 .