show that p= 4/5q if the equation px^2+3px+p+q=0 where p is not equal to 0 , has two equal real roots

Answer 1

for 2 equal roots, b^2 - 4ac = 0
9p^2 - 4(p)(p+q) = 0
9p^2 - 4p^2 - 4pq = 0
5p^2 - 4pq = 0
p(5p - 4q) = 0
p = 0 or p = 4q/5
but p≠0 or else we don't have a quadratic,
so

p = (4/5)q