A math teacher wrote x^2+bx+c=0 on the board and asked students to find the two real roots. Alice miscopied one of the coefficients and found that 1 and 4 were the roots. Andy miscopied a different coefficient and found that -2 and 3 were the roots. Determine the roots to the equation the teacher wrote.

Question

A math teacher wrote x^2+bx+c=0 on the board and asked students to find the two real roots.  Alice miscopied one of the coefficients and found that 1 and 4 were the roots. Andy miscopied a different coefficient and found that -2 and 3 were the roots. Determine the roots to the equation the teacher wrote.

MathMate · Answer

Alice's version:
b=-1-4=-5, c=1*4=4
Andy's version:
b=2-3=-1, c=-2*3=-6

SO the equation could be either:
x²-5x-6=0 ...(a)
or
x²-x+4=0 ...(b)
Equation (b) has no real roots, so
the equation must be (a), or
(x-6)(x+1)=0
giving x=6 or x=-1 as roots.