Question

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

• A. $x^2-10x+9=0$
• B. $x^2+10x+9=0$
• C. $x^2-10x+16=0$
• D. $x^2-8x-9=0$
• E. none of these

Answer 1

Answer: (A)

$x^2-10x+9=0$

Let the true equation be $x^2+bx+c=0$, the equation obtained by the first student be $x^2+bx+c=0$, and the equation obtained by the second student be $x^2+b^{\prime }x+c=0$

$x^2+bx+c^{\prime }=x^2-10x+16=0$ and $x^2+b^{\prime }x+c=x^2+10x+9=0$

$\therefore x^2+bx+c=x^2-10x+9=0$