Prove that the equation x^2+ 2px + 2q=0 can`t have rational roots if p and q are odd integers.
Sunny Gupta , 6 Years ago
Grade 11
Algebra> Prove that the equation x^2+ 2px + 2q=0 c...
2 Answers
Arun
Last Activity: 6 Years ago
the discriminant is
b^2-4ac = (2p)^2 – 8q – 4(p^2-2q)
as p and q are odd
p^2-2q = (2s+1)^2 – 2(2t+1) = (4s^2+ 4s+1) – (4t+2) =(4s^2 + 4s – 4t -1)
so discriminant cannot be a perfect square so there is no rational root
b^2-4ac = (2p)^2 – 8q – 4(p^2-2q)
as p and q are odd
p^2-2q = (2s+1)^2 – 2(2t+1) = (4s^2+ 4s+1) – (4t+2) =(4s^2 + 4s – 4t -1)
so discriminant cannot be a perfect square so there is no rational root
Sunny Gupta
Last Activity: 6 Years ago
Why can`t be not a perfect square? last step i can`t understand.
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