Question
If x2−gx+3=0 and 2x2−6x+g=0 have a common root, then find the value(s) of the common root.
Answer: Option C
:
C
If two equations have a common root then they can be found by equating them:
When we equate we get x2+x(g−6)+(g−3)=0
Now the Determinant of this equation has to be equal to 0
(g−6)2−4(1)(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.
x2−gx+3=0 is equation 1.
2x2−6x+g=0 is equation 2.
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:
C
If two equations have a common root then they can be found by equating them:
When we equate we get x2+x(g−6)+(g−3)=0
Now the Determinant of this equation has to be equal to 0
(g−6)2−4(1)(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.
x2−gx+3=0 is equation 1.
2x2−6x+g=0 is equation 2.
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