Question

form a polynomial whose zero are
$\frac{3 - \sqrt{3} }{5} and \frac{3 + \sqrt{3} }{5}$
​

Answer 1

Answer:

$25x^2 - 30x+6=0$

Step-by-step explanation:

given$zeros=\dfrac{3-\sqrt{3}}{5}\:and\:\dfrac{3+\sqrt{3}}{5}\\\\\alpha +\beta =\dfrac{-b}{a}\\\\\alpha *\beta =\dfrac{c}{a}\\\\\implies\:\dfrac{3-\sqrt{3}}{5}+\dfrac{3+\sqrt{3}}{5}=\dfrac{6}{5}=\alpha +\beta =\dfrac{-b}{a}....equ(1)\\\\and\:\dfrac{3-\sqrt{3}}{5}*\dfrac{3+\sqrt{3}}{5}=\dfrac{9-3}{25}=\dfrac{6}{25}.....equ(2)\\\\multiply\:5\:in\:equ\:(1)\\\implies\:\dfrac{6*5}{5*5}=\dfrac{30}{25}=\dfrac{-b}{a}\\\\\implies\:a=25,\:b=-30,\:c=6\\\\\implies25x^2 - 30x+6=0$