Question 1184308


If {{{px^2 + 3px + p + q = 0}}}  has two equal roots, then the left -hand side can be written as {{{p(x - alpha)^2 = 0}}}, where {{{alpha}}} is the real double root.


===> {{{p(x-alpha)^2 = p(x^2 -2*alpha*x + alpha^2) = px^2 -2p*alpha*x + p*alpha^2)}}}


===> {{{3p = -2p*alpha}}}  and {{{p + q = p*alpha^2}}}.


The first equation implies that {{{alpha = -3/2}}}.


===> {{{p + q = (9/4)p}}}  ===> {{{q = (5/4)p}}}