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Question

In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds 9 and 1 for roots. The correct equation is

A
x210x+9=0
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B
x2+10+9=0
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C
x210x+16=0
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D
x28x9=0
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Solution

The correct option is A x210x+9=0
Let the actual quadratic equation be x2+bx+c=0
First student makes a mistake in constant. Let's say he took the constant as d
Hence the quadratic equation for the first student becomes x2+bx+d=0
The roots for this equation are 8 and 2
Sum of roots =b=10
b=10
Product of the roots =16=d
d=16
The second student makes a mistake in the coefficient of first degree term. Let's say he considered it to be e instead of b
The equation becomes x2+ex+c=0 with roots 9,1
Sum of the roots =10=e
e=10
Product of the roots =9=c
c=9
Hence the actual quadratic equation becomes x210x+9=0

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