If (x-3) and (x-1/3) are both factors of ax^2+5x+b,then show that a=b

Answers (1)

If (x-3) and (x-1/3) are both factors of f(x) = ax2+5x+b,

then f(3) = 0 and  f(1/3) =0

f(3) = a(3)2+5(3)+b = 0  => 9a + b + 15 = 0 ..(i)

f(1/3) = a(1/3)2+5/3+b =0  => a + 9b + 15 =0 ...(ii)

Equation (i) - Equation (ii)

9a + b + 15 - a - 9b - 15 =0

8a - 8b = 0  => a=b

Hence proved 

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