- #1
Vishalrox
- 20
- 0
theory of quadratic equations...
theres a quadratic equation lx^2 + nx + n where its roots are in the ratio p:q .we need to prove that
√(p/q) + √(q/p) + √(n/l) = 0
what i did was..i introduced a proportionality constant k... so pk + qk = -(n/l)
while pq(k^2) = n/l ...solved these two equations and got the value of k as -(p+q)/pq...
and i substituted..i got the roots of the equation in terms of p and q...i got the value of n/l = ((p+q)^2)/pq...coming to the equation which we need to prove...i squared the whole Left Hand Side...expanded it...and substituting whatever i got...i got..4((p+q)^2)/pq...i.e.,i got 4(n/l)...so now we got to prove that 4(n\l) is 0...but if 4(n\l) = 0 then n/l will be 0...which in turn accounts for n = 0...which lands us into a trivial case...all roots and all other coefficients other than leading coefficient (l) to be 0...but i don't think that would be the right way to solve this problem...can anyone help me on this on a different method...?
theres a quadratic equation lx^2 + nx + n where its roots are in the ratio p:q .we need to prove that
√(p/q) + √(q/p) + √(n/l) = 0
what i did was..i introduced a proportionality constant k... so pk + qk = -(n/l)
while pq(k^2) = n/l ...solved these two equations and got the value of k as -(p+q)/pq...
and i substituted..i got the roots of the equation in terms of p and q...i got the value of n/l = ((p+q)^2)/pq...coming to the equation which we need to prove...i squared the whole Left Hand Side...expanded it...and substituting whatever i got...i got..4((p+q)^2)/pq...i.e.,i got 4(n/l)...so now we got to prove that 4(n\l) is 0...but if 4(n\l) = 0 then n/l will be 0...which in turn accounts for n = 0...which lands us into a trivial case...all roots and all other coefficients other than leading coefficient (l) to be 0...but i don't think that would be the right way to solve this problem...can anyone help me on this on a different method...?