SOLUTION: If the quadratic equation p^2x^2 + 4qx + 25 = 0 has real and equal roots such that p>0 and q>0, find p:q.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If the quadratic equation p^2x^2 + 4qx + 25 = 0 has real and equal roots such that p>0 and q>0, find p:q.      Log On


   

Question 857219: If the quadratic equation p^2x^2 + 4qx + 25 = 0 has real and equal roots such that p>0 and q>0, find p:q.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This requires discriminant equal to zero.

Discriminant=%284q%29%5E2-4%2A%28p%5E2%29%2A25=0
%284q-10p%29%284q%2B10p%29=0
%282q-5p%29%282q%2B5p%29=0
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One or the other of each binomial factor is zero for the product to be zero.
If 2q-5p=0%2C+then+2q=5p
5p=2q
5p%2Fq=2
highlight%28p%2Fq=2%2F5%29--------THE ANSWER
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If 2q%2B5p=0, then 2q=-5p
5p=-2q
5p%2Fq=-2
p%2Fq=-2%2F5 -----Which we do NOT want because it is contrary to the specifications.