If (x-3) and (x-1/3) are the factors of ax^2+5x+b, then show that a=b
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f(x) = ax² + 5x +b
now a/q (x-3),(x-1/3) are the factors of f(x) , that implies that
f(3) = a(3)² + 5(3) + b = 0 ⇒ 9a + 15 + b = 0 ............(1)
f(1/3) = a(1/3)² + 5(1/3) + b = 0 ⇒ a/9 + 5/3 + b = 0 ⇒ a + 15 + 9b = 0 .....(2)
sutracting 1 from 2
8a - 8b = 0 ⇒ a = b Hence proved.
now a/q (x-3),(x-1/3) are the factors of f(x) , that implies that
f(3) = a(3)² + 5(3) + b = 0 ⇒ 9a + 15 + b = 0 ............(1)
f(1/3) = a(1/3)² + 5(1/3) + b = 0 ⇒ a/9 + 5/3 + b = 0 ⇒ a + 15 + 9b = 0 .....(2)
sutracting 1 from 2
8a - 8b = 0 ⇒ a = b Hence proved.
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