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.)

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) (Show Source): You can put this solution on YOUR website!
Distance between P(a,3) and Q(6,2a) is

=
=
For this distance to be greater than 29;

=>
=>
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.

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