Question

find a quadratic polynomial whose sum and product of zeroes are
$2 \sqrt{3}$
And
$- 5 \sqrt{3}$

Answer 1

$sum \: of \: zeroes \: = 2 \sqrt{3} \\ \\ product \: of \: zeroes \: = - 5 \sqrt{3}$
Required polynomial = x^2 - (sum of zeroes)x + Product of zeroes

$= {x}^{2} - 2\sqrt{3} x - 5 \sqrt{3}$

Answer 2

Hii friend,

alpha + bet = 2✓3

Alpha × Beta = -5✓3

Therefore,


Quadratic polynomial = X²-(Alpha+Beta)X + Alpha × Beta

= X²-(2✓3)X + (-5✓3)

= X²-2✓3X - 5✓3 is the required polynomial.


HOPE IT WILL HELP YOU..... :-)