Question

Find a quadratic equation polynomial I whose whose sum and product of its zeros are 1 by 4 and -1 respectively ​

Answer 1

Answer:

Here alpha +beta = 1/4

and alpha ×beta = -1

Then quadratic equation=x^2-(alpha+beta)x +alpha×beta

=x^2-1/4x+(-1) =0

=4x^2-x-4=0

Answer 2

Answer:

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