Because the equation has equal roots
Given that has equal roots
and and are positive,
find the ratio
and solve the equation.
(I was able to deduce the relation , but how is the ratio further on calculated?
How are the value of and deduced in such a way that substituting their values would solve the equation? )
(The answers provided are and .)
Another way to do this: if we call the two equal roots "r" then we must have
and so must have and . That second equation reduces to so that r= 1 or r= -1. In order that p and q both be positive, we must have r= 1 and then we have so that .