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Solve the following:

qsnImg
Asked by Anish 2nd September 2018, 12:22 AM
Answered by Expert
Answer:
begin mathsize 18px style straight f open parentheses straight x close parentheses equals ax squared plus bx plus straight c
both space roots space are space irrational space so space for space any space rational space number space straight lambda
open vertical bar straight f open parentheses straight lambda close parentheses close vertical bar greater than 0
open vertical bar ap squared over straight q squared plus bp over straight q plus straight c close vertical bar greater than 0
1 over straight q squared open vertical bar ap squared plus bpq plus cq squared close vertical bar greater than 0
open vertical bar ap squared plus bpq plus cq squared close vertical bar greater than 0
here space straight a comma space straight p comma space straight q comma space straight b space comma space straight c space are space integers
so space
open vertical bar ap squared plus bpq plus cq squared close vertical bar greater or equal than 1
so
1 over straight q squared open vertical bar ap squared plus bpq plus cq squared close vertical bar greater or equal than 1 over straight q squared

open vertical bar straight f open parentheses straight lambda close parentheses close vertical bar greater or equal than 1 over straight q squared
end style
Answered by Expert 4th September 2018, 3:29 PM
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