If both (x+2)and (2x+1) are the factors of ax 2 + 2x + b, prove that a-b=0
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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)
∴, 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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