Don
had Sheri list what a, b and c are in x2
- 5x + 6 = 0; a = 1, b= Sheri uses the quadratic formula to find the missing base for Don's age
Don had Sheri solve x2 - 5x + 6 = 0 using the quadratic formula. She knew what the two answers were {2,3}, but Don helped her to substitute in the formula, then get the two answers:
Don
had Sheri list what a, b and c are in x2
- 5x + 6 = 0; a = 1, b=
- 5 and c=6. a=1 was not obvious; they talked about what times x2 = x2 ? 1. Don substituted these values of a, b, and c into the formula:
They
got 
The ' means
"plus or minus" and this gives the two answers as shown above. Sheri
then solved another quadratic equation (for which she knew the answers), using
the using the formula, then solved x2
+ x + 4 = 71 or x2 + x - 67 = 0 to
find the base for Don's age:
These two exact answers are approximately 7.700609733... and -8.700609733. Sheri got the first answer, but didn't have time to get the second one. Notice that in using the calculator to do find the base earlier, Sheri got 7.7, which was very close to the answer using the quadratic equation. So Don's "age" of 114 is in base 7.7 to get his real age of 71!
There are many good questions that Don thinks of now..what do you think?