Question

find the quadratic polynomial,the sum and product of whose zeroes are root 2 and 1/√3 respectively.find its zeroes

Answer 1

$Heya$‼

$As\:we\:know,$
$Quadratic\:Polynomial=ax^2+bx+c$

$Given \:that,$
$Sum=\sqrt{2}$

$Product=\frac{1}{\sqrt{3} }$

$Now,$
$Sum\:of\:zeroes=\frac{-b}{a}$
$\sqrt{2}= \frac{-b}{a}$
$\frac{\sqrt{2}*\sqrt{3} }{\sqrt{3} }= \frac{-b}{a}$

$Product\:of\:zeroes=\frac{c}{a}$
$\frac{1}{\sqrt{3} } = \frac{c}{a}$

$So,a=\sqrt{3},b=-\sqrt{2}\:and\:c=1$

$Quadratic \:Polynomial$
$=\sqrt{3}x^2-\sqrt{2}x-1$