Question

Find a quadratic polynomial sum of whose zeroes is 4 and product of zeroes is-1/4

Answer 1

Answer:

$p(x) = x ^{2} - ( \alpha + \beta )x + \alpha \beta \\ p(x) = x ^{2} - 4 - \frac{1}{4 } \\ p(x) = 4 {x}^{2} - 4 - 1$

I hope you understood this sum

Answer 2

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