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Question

In solving a problem, one student made a mistake in the coefficient of the first degree term and obtained -9 and -1 as the roots. Another student made a mistake in the constant term of the equation and obtained 8 and 2 for the roots. Assuming the coefficient of x2 as 1, the correct equation was-


A

x2 + 10 x + 9 = 0

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B

x2 - 10x +9 = 0

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C

x2 - 10x + 16 = 0

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D

None of these

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Solution

The correct option is B

x2 - 10x +9 = 0


According to the first set of solutions, equation:

(x + 9)(x + 1) = 0

x2 + 10x + 9 = 0 [Constant term is correct]

According to the second set of solutions:

(x - 8)(x - 2) = 0

x2 -10x + 16 = 0 [Coefficient of x is correct]

So, the correct equation is x2 - 10x + 9 = 0 [Taking the correct terms from above equations]


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