Problem: If x2−5x+6<0 and P=x2+5x+6 then
Answer Choices:
A. P can take any real value
B. 20< P <30
C. 0< P <20
D. P<0
E. P>30
Solution:
Since x2−5x+6=(x−3)(x−2)<0, we have 2<x<3. Since P=x2+5x+6, then P<32+5⋅3+6=30 and P>22+5⋅2+6=20, that is 20<P<30.