SOLUTION: x^2-14x+48<0 The answer choices are: A (4,12), B (6,8), C (-infinity,6) U (8, infinity), D (-infinity,6] U [8, infinity)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: x^2-14x+48<0 The answer choices are: A (4,12), B (6,8), C (-infinity,6) U (8, infinity), D (-infinity,6] U [8, infinity)      Log On


   

Question 536670: x^2-14x+48<0
The answer choices are: A (4,12), B (6,8), C (-infinity,6) U (8, infinity), D (-infinity,6] U [8, infinity)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
IF YOU CAN FACTOR (using the quadratic formula to help is allowed)
x%5E2-14x%2B48=%28x-8%29%28x-6%29 so it will be positive for x<6 and for x>8, zero at x=6 and x=8 , and negative in between.
IF YOU WILL NOT FACTOR
The coefficient of the x%5E2 term is positive (+1), so the parabola opens up (smiling shape). A parabola with that shape might be negative somewhere in the middle, but will definitely have positive y values at both ends. That eliminates answers C and D.
For x=10 x%5E2-14x%2B48=10%5E2-14%2A10%2B48=100-140%2B48=8
and that eliminates answer A.