Question

find a quadratic polynomial whose sum and product of its zeroes of its zeroes are 1/4 and -1 respectively.​

Answer 1

sum of zeroes = 1 / 4

product of zeroes = -1

quadratic polynomial = k ( x² - (sum of zeroes)x + product of zeroes)

= k ( x² - 1 / 4x - 1 )

here lcm = 4

so k = 4

= 4 ( x² - 1 / 4 x -1 )

= 4x² - 1x -4

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Answer 2

Answer:

$Given, \: Sum \: of \: zeroes \: = 1/4</p><p> \\ and \: product \: of \: zeros = \: -1 \\ </p><p>Then, \: the \: quadratic \: polynomial \\ = k \: [ {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes ] \\ k( {x}^{2} - ( \frac{1}{4} )x - 1 \\ = k( {x}^{2} - \frac{x}{4} - 1) \\ = k( \frac{4 {x}^{2} - x - 4 }{4 } ) \\ If \: k = 4, \: then \: the \: required \: quadratic \: polynomial \: is \\⇒ \: 4 {x}^{2} - x - 4</p><p>$