QJEEM08Ma4193: JEE Main 2008 Mathematics - Class 11 JEEM08Ma4193 Solution: The quadratic equations and have one root in common. The other…

Question

Verified Solution • 2025–26 Session moderate

The quadratic equations

{x^2} - 6x + a = 0

and

{x^2} - cx + 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

Accepted Answer

Let the roots of equation

{x^2} - 6x + a = 0

be

\alpha

and

4

\beta

and that of the equation

{x^2} - cx + 6 = 0

be

\alpha

and

3\beta .

Then

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha + 4\beta = 6;\,\,\,\,\,\,\,4\alpha \beta = a

and

\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha + 3\beta = c;\,\,\,\,\,\,\,3\alpha \beta = 6

\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a = 8

\therefore

The equation becomes

{x^2} - 6x + 8 = 0

\Rightarrow \left( {x - 2} \right)\left( {x - 4} \right) = 0

\Rightarrow

roots are

2

and

4

\Rightarrow \alpha = 2,\beta = 1

\therefore

Common root is

2.

Step-by-Step Verified Solution