Q.The value of parameter a for which the quadratic equations (1-2a)x²-6ax-1=0 and ax²-x+1=0 have atleast one common root,are-

(a)0,1/2   (b)1/2,2/9  (c)2/9  (d)1/3,1/2,2/9.

give corr. solution for ur answer.

The ans is B

if it is ok.. i will post the solution..

At least one common root means it can have one or two common roots.

If and have a common root then

If both roots are common then

a₁/a₂ = b₁/b₂ = c₁/c₂

If we put values 2nd condition is not true.

If we put the values and solve for a using 1st condition we get a = 2/9.

so c) is the correct option.

If you are good at math directly put the options in equations and check if there is any common root or not.

I did in this way.

1/2 was common in three of the options so put a = 1/2 in both equations and you'll find that there is no common root. So all the three options are wrong.

so I concluded option c is correct.