if (x-2)and(2x-1)are factors of ax^2+5x+b show that a-b=0

Asked by Anishma Joseph | 15th Jul, 2013, 07:10: PM

Expert Answer:

Since, (x-2)and(2x-1)are factors of f(x) =ax^2+5x+b
hence, f(2) = f(1/2) = 0
f(2) = a(2)^2 + 5(2) + b = 0
4a + 10 + b = 0 (1)
 
Also, f(1/2) = a(1/2)^2 + 5*1/2 + b  = 0
a + 10 + 4b = 0 (2) 
 
Subtracting 1 and 2
3a -3b = 0
a-b = 0
Hence proved. 
 

Answered by  | 15th Jul, 2013, 09:32: PM

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