Question

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

Answer 1

put x=3 and x= 1/3 in the equation

>> a.9 + 12 + b =0

and a. (1/9) + 4/3 + b = 0

solving these two eqn.

9a + 12 = a/9 + 4/3
81a + 108 = a + 12
80a = - 96

or a = -96/80 = -12/10 = -6/5

and b = -12 - 9a = -12 -9(-6/5) = -12 + 54/5 = - 6/5

so, a-b = -6/5 - (-6/5) = 0

hence proved :)



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