Question

ffind quadretic polynomial whose zeros are 3−√3÷5 and 3+√3÷5

Answer 1

Answer:

Let the zeroes be a, b = 3 -√3÷5,3 + √3÷5

To find a polynomial with given zeroes,

p(x) = x² - x(a + b) + ab

= x² - x[(3- √3 + 3 + √3)/5] + (3 - √3)(3+√3)/25

= x² - 6x/5 + (9 - 3)/25

= x² - 6x/5 + 6/25

Multiplying everything by 25,

= 25x² - 30x + 6

I have included another method in the attachment, just for fun. I don't recommend you to use it though.....

Sidenote: In the other method I included, if you multiply everything by 10, you would get the same answer that I got by the normal method.