Question

If $x^2-gx+3=0$ and $2x^2-6x+g=0$ have a common root, then find the value(s) of the common root.

• A. 1
• B. 2
• C. 3
• D. none of these
  

Answer 1

The correct option is C

3

If two equations have a common root then they can be found by equating them:
When we equate we get $x^2+x(g-6)+(g-3)=0$
Now the Determinant of this equation has to be equal to 0
$(g-6{)}^2-4(1\left)\right(g-3)=0$
We get the values of g= 4 or 12

Re-substituting in the original equation we see that only g=4 will satisfy the equation

i.e You will get the roots to be 1,2 and 1,3 hence 1 is the common root.

$x^2-gx+3=0$ is equation 1.
$2x^2-6x+g=0$ is equation 2.