In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -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

A) \( \Large x^{2}+10x+9=0 \)
B) \( \Large x^{2}-10x+16=0 \)

C) \( \Large x^{2}-10x+9=0 \)
D) None of the above.

Correct answer:
C) \( \Large x^{2}-10x+9=0 \)

Description for Correct answer:
When mistake is done in first degree term, the roots of the equation are -9 and -1. Therefore, Equation is

\( \Large \left(x + 1\right) \left(x + 9\right) = x^{2} + 10x + 9 \) ...(i)

When mistake is done in constant term, the roots of equation are 8 and 2.

Therefore, Equation is

\( \Large \left(x - 2\right) \left(x - 8\right) = x^{2} + 10x + 16 \) ...(ii)

Therefore, Required equation from Eqs. (i) and (ii) is

= \( \Large x^{2} - 10x + 9 \)

Also we see in both the cases 1st degree term is same with opposite sign i.e., in such questions we should take data from given conditions and find the correct equation.

Please provide the error details in above question

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