Q. 244.0( 2 Votes )

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Answer :

Let p(x) = ax2 + 2x + b


As (x + 2) and (2x + 1) are factors of p(x) hence each will divide p(x) leaving remainder as 0


Let us use the remainder theorem which states that if (x – a) divides a quadratic polynomial p(x) then p(a) = 0


First a = –2


p(a) = a(–2)2 + 2(–2) + b


0 = 4a – 4 + b


b = 4 – 4a …(i)


Now a = –1/2


p(a) = a(–1/2)2 + 2(–1/2) + b



Multiply whole equation by 4


0 = a – 4 + 4b


4b = 4 – a …(ii)


Subtract (i) from (ii)


4b – b = (4 – a) – (4 – 4a)


3b = 4 – a – 4 + 4a


3b = 3a


a = b


a – b = 0


Hence proved


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