Question

find the quadratic polynomial whose sum and product of its zero are 1/4 and -1
​

Answer 1

Step-by-step explanation:

sum of the zeroes=1/4

product of zeroes = -1

k={x square - x (alpha + beta)+alpha× beta}

k={xsquare -x (1/4)+(-1)}

k={xsquare -x/4 -1}

k={4xsquare-x-4}

after sub k=4

equation will be 4xsquare -×-4

Answer 2

Answer:

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