In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtain -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was

When mistake is done in first degree term, the roots of the equation are -9 and -1.
∴ Equation
(x+ 1) (x + 9) = x² + 10x + 9 ...(i)
When mistake is done in constant term, the roots of equation are 8 and 2.
∴ Equation is
(x - 2) (x - 8) = x² - 10x + 16 .....(ii)
∴ Required equation from Eqs. (i) and (ii) is
= x² - 10x + 9
Also we see in both the cases 1st degree term is same with oposite sign i.e., in such questions we should take data from given conditions and find the correct equation.