Problem: 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:
Answer Choices:
A. x2−10x+9=0
B. x2+10x+9
C. x2−10x+16=0
D. x2−8x−9=0
E. none of these
Solution:
Let the true equation be x2+bx+c=0, the equation obtained by the first student be x2+bx+c′=0, and the equation obtained by the second student be x2+b′x+c=0.
x2+bx+c′=x2−10x+16=0 and x2+b′x+c=x2+10x+9=0.∴x2+bx+c=x2−10x+9=0.