SOLUTION: For what values of "a" is the distance between P(a, 3) and Q(6, 2a) greater than 29? (Enter your answer using interval notation.)

Algebra ->  Graphs -> SOLUTION: For what values of "a" is the distance between P(a, 3) and Q(6, 2a) greater than 29? (Enter your answer using interval notation.)      Log On


   

Question 993287: For what values of "a" is the distance between P(a, 3) and Q(6, 2a) greater than 29?
(Enter your answer using interval notation.)
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Distance between P(a,3) and Q(6,2a) is
sqrt%28%286-a%29%5E2+%2B+%282a-3%29%5E2%29
= sqrt%28a%5E2-12a%2B36+%2B+4a%5E2-12a%2B9%29
= sqrt%285a%5E2-24a%2B45%29
For this distance to be greater than 29;
sqrt%285a%5E2-24a%2B45%29+%3E+29
=> 5a%5E2-24a%2B45+%3E+841
=> 5a%5E2-24a-796+%3E+0
Solving the quadratic we get roots as -10.44 and 15.24
Since coefficient of a^2 is positive, the graph is opening upwards
So the value of this quadratic is negative between these two roots.
So the required value of a for the quadratic to be positive, is
All values of a except [-10.44,15.24] range.