Two candidates attempt to solve the equation 
. One starts with a wrong value of 
and finds the roots to be 2 and 6 and the other starts with a wrong value of 
and find the roots to be 2 and -9. The roots of the original equation are
Text Solution
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Let the correct equation be 
Roots found by the first student are 6 and 2.
Their sum 
and the product 
So, (i) reduces to 
But he has committed mistake only in the coefficient of 
i.e. in 
. So 
remains equal to 12 while 
in the actual equation has been taken wrongly by the first student.
Now roots found by the second student are 2 and -9.
Their sum 
and the product
But he has committed mistake only in the constant term i.e. in 
. So 
remains equal to 7.
Hence correct equation from (i) is 
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