Question

The price for one ticket of cinema is rs. (x2 - 3x + 9). How many tickets are purchased in rs. (x4 + 9x2 + 81)? 5. Find the zeroes of the cubic polynomial p(x) = x + 7x2 + 5x -1.
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answers with a detailed explanation is truly appreciated ​

Answer 1

SOLUTION

TO DETERMINE

The price for one ticket of cinema is

$\sf{Rs. \: \: ( {x}^{2} - 3x + 9) }$

How many tickets are purchased in

$\sf{Rs. \: \: ( {x}^{4} + 9 {x}^{2} + 81) }$

EVALUATION

Here

$\sf{ {x}^{4} + 9 {x}^{2} + 81}$

$\sf{ = {x}^{4} + 18 {x}^{2} + 81 - 9 {x}^{2} }$

$\sf{ = {( {x}^{2} )}^{2} + 2. {x}^{2}.9 + {(9)}^{2} - {(3x)}^{2} }$

$\sf{ = {( {x}^{2} + 9 )}^{2} - {(3x)}^{2} }$

$\sf{ = ( {x}^{2} + 9 + 3x)( {x}^{2} + 9 - 3x ) }$

$\sf{ = ( {x}^{2} + 3x + 9)( {x}^{2} - 3x + 9 ) }$

Now The price for one ticket of cinema is

$\sf{Rs. \: \: ( {x}^{2} - 3x + 9) }$

Hence the total number of tickets purchased

$\displaystyle \sf{ = \frac{ \sf{ {x}^{4} + 9 {x}^{2} + 81}}{ {x}^{2} - 3x + 9 } }$

$\displaystyle \sf{ = \frac{ ({x}^{2} + 3x + 9)({x}^{2} - 3x + 9 ) }{ {x}^{2} - 3x + 9 } }$

$\sf{ = {x}^{2} + 3x + 9 }$

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