A and B solve an equation x 2 + px + q = 0. In solving A commits a mistake in reading p and finds the roots 2 and 6 and B commits a mistake in reading q and finds the roots 2 and – 9. Find the correct roots.
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Sol. Let the roots of the quadratic equation 
be 
and 
. According to the given condition, A starts with a wrong value of 
and obtains the roots as 2 and 6. But this time, the value of q is correct.
Product of roots 
.
According to the second condition, 
starts with a wrong value of 
and obtains the roots as 2 and -9 . But this time, the value of 
is correct.
∴ Solving equations (i) and (ii), we get 
and 
.
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