Question

If both(x+2) and (x+1) one factor of ax square+2x+b then find the value of a minus b​

Answer 1

Answer:

If (x+2) and (2x+1) are the factors of f(x)=ax²+2x+b then x=-2 and x=-1/2.

∴, a(-2)²+2(-2)+b=0

or, 4a-4+b=0

or, 4a+b=4 -----------(1) and

a(-1/2)²+2(-1/2)+b=0

or, a/4-1+b=0

or, a-4+4b=0

or, a+4b=4 -----------(2)

Subtracting (2) from (1) we get,

4a+b-(a+4b)=4-4

or, 3a-3b=0

or, a-b=0 (Proved)

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