Question

The values of a for which the quadratic equations $(1-2a)x^2-6ax-1=0$ and $a{x}^2-x+1=0$ have at least one root is common are:

• A. $\frac{1}{2},\frac{2}{9}$
• B. $0,\frac{1}{2}$
• C. $\frac{2}{9}$
• D. $0,\frac{1}{2},\frac{2}{9}$

Answer 1

The correct option is C $\frac{2}{9}$

For $a=0$ or $a=\frac{1}{2}$ , one of the quadratic equations becomes linear, so $a\ne 0,a\ne \frac{1}{2}$.
Hence the only answer is $a=\frac{2}{9}$