Question

find a quadratic polynomial whose zeroes are
$(3 + \sqrt{2} \div 3 - \sqrt{2)}$
and
$(3 - \sqrt{2} \div 3 + \sqrt{2} )$
​

Answer 1

Two roots are given, rationalize both of them and bring to simpler form.

Then as you know in an quadratic eqn. ,

Sum of roots= -b/a

product of roots = c/a

Now form the quadratic eqn. --- >

x^2+ sum of roots*(x) + product of roots =0

--> x^2 + (-b/a) *x + (c/a) =0