1.

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Answer»

Step-by-step EXPLANATION:

Let \: \alpha = \frac{1}{2} \\: \beta = \frac{-3}{2}\: and\:\\ p(x)= 4x^{2}+4x-3 --(1)

Now ,

i ) Put\: \alpha\: in \:equation\: (1), \:we \:get\\p(\frac{1}{2})=4(\frac{1}{2})^{2}+4(\frac{1}{2})-3\\=4\times \frac{1}{4}+2-3\\=1+2-3\\=0\\

THEREFORE,

p(\frac{1}{2})=0

\alpha \: is \: a zero\: of \:p(x)

ii) Put\: \beta\: in \:equation\: (1), \:we \:get\\p(\frac{-3}{2})=4(\frac{-3}{2})^{2}+4(\frac{-3}{2})-3\\=4\times \frac{9}{4}-6-3\\=9-6-3\\=0\\

Therefore,

p(\frac{-3}{2})=0

\beta \: is \: a zero\: of \:p(x)

III) COMPARE 4x²+4x-3 with

ax²+bx+C , we get

a=4, b=4, c =-3

Sum \:of \:the \: zeroes \\=\frac{1}{2}+\frac{-3}{2}\\=\frac{1-3}{2}\\=\frac{-2}{2}\\=\frac{-1}{1}\\=\frac{-coefficient\:of\:x}{coefficient\:of \:x^{2}}

Product\:of\:zeroes\\=\frac{1}{2}\times \frac{-3}{2}\\=\frac{-3}{4}=\frac{constant}{coefficient\:of\:x^{2}}

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