Q. 104.2( 31 Votes )

If x = –1/2 is a zero of the polynomial p (x) = 8x3ax2x + 2, find the value of a.

Answer :

Concept Used:


If x = a is a root of a polynomial f(x), then f(a) = 0


Explanation:


We have,


p (x) = 8x3ax2x + 2


Put x = – 1/2


p (– 1/2 ) = 8 (– 1/2 )3 – a (– 1/2 )2 – (– 1/2 ) + 2


= 8 × – 1/8 – a × 1/4 + 1/2 + 2


= –1 – a/4 + 1/2 + 2



Given that,


x = – 1/2 is a root of p (x)


p (– 1/2 ) = 0


Therefore,




a = 6


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