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Question
If `x = −1/2` is a zero of the polynomial `p(x)=8x^3-ax^2 -+2` find the value of a.
Solution
we have `p(x)=8x^2-ax^2-x=2`
put `x=-1/2`
`⇒p(-1/2)=8xx(-1/2)^3-ax(-1/2)^2-(-1/2)+2`
`=8xx-^1/8-axx1/4+1/2+2`
`=-1-a/4+1/2+2`
`=3/2-a/4`
giventhat `x=(-1)/2`is a root of p(x)
`⇒ p(-1/2) = 0`
`∴ 3/2 - a/4 = 0 ⇒ a/4=3/2⇒a=3/2xx4^2`
`⇒a=6`
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