Solve a quadratic equation using Vieta's formulas
Python - 202 200 bytes
2 bytes saved thanks to @FryAmTheEggman.
from fractions import*;f=Fraction
lambda a,b,c:&quot;\n&quot;.join([&quot;x=%s?%dx^2+%dx+%d=%s&quot;%(i,a,b,c,a*i*i+b*i+c)for i in[f(1,a),f(-1,a),f(c,a)]]+[&quot;r%d=%s&quot;%((3-i)/2,f(i*(b*b-4*a*c)**.5-b)/f(2*a))for i in[1,-1]])