Dear student We have,3a-2b+5c=0⇒35a-25+c=0Therefore, ax+by+c=0 always passes through the point 35,-25So, α=35 and β=-25and 5(α-β)=535--25=51=5 Regards

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Dear student

W e h a v e, 3 a - 2 b + 5 c = 0 \Rightarrow (\frac{3}{5}) a - (\frac{2}{5}) + c = 0 T h e r e f o r e, a x + b y + c = 0 a l w a y s p a s s e s t h r o u g h t h e p o i n t (\frac{3}{5}, \frac{- 2}{5}) S o, α = \frac{3}{5} a n d β = \frac{- 2}{5} a n d 5 (α - β) = 5 (\frac{3}{5} - (\frac{- 2}{5})) = 5 (1) = 5

Regards

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