SOLUTION: Given that the equation px^2 + 3px + p + q = 0,where p is not = 0, has two equal real roots,find q in terms of p

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Question 1184307: Given that the equation px^2 + 3px + p + q = 0,where p is not = 0, has two equal real roots,find q in terms of p
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given that the equation px%5E2+%2B+3px+%2B+p+%2B+q+=+0,where p+%3C%3E+0, has two equal real roots, find q in terms of p.

the equation has two equal real roots if discriminant is equal to zero
b%5E2-4ac=0
px%5E2+%2B+3px+%2B+p+%2B+q+=+0 in your case a=p, b=3p, and c=+p+%2B+q+
%283p%29%5E2-4%2Ap%2A%28p+%2B+q%29=0
9p%5E2-+%284p%5E2+%2B+4pq%29=0
9p%5E2-+4pq-+4p%5E2=0
5p%5E2-+4pq=0...factor
p+%285p+-+4q%29+=+0

solutions:
p=0-> exclude because gien that p+%3C%3E+0
%285p+-+4q%29+=+0=>5p+=+4q=>5p+=4q=>q=%285%2F4%29p++

px%5E2+%2B+3px+%2B+p+%2B+q+=+0.......substitute q=%285%2F4%29p+
px%5E2+%2B+3px+%2B+p+%2B+%285%2F4%29p+=+0.....both sides multiply by 4
4px%5E2+%2B+12px+%2B+4p+%2B+5p+=+0
4px%5E2+%2B+12px+%2B+9p+=+0
check if discriminant is equal to zero:
%2812p%29%5E2-4%284p%29%289p%29=0
144p%5E2-144p%5E2=0
0=0=>true