Question

Form a quadratic polynomial whose zeroes are (3 - √3)/5 & (3 + √3)/5.

Explain clearly.

Points : 15☺

Answer 1

step 1 :-
sum of roots = (3 -√3)/5 + (3 +√3)/5
=6/5

products of roots = (3-√3)(3+√3)/5×5
=(9-3)/25 = 6/25

step 2 :-
use ,
x² -( sum of roots )x + products of roots =0

x² -(6/5) x +(6/25) =0

25x² -30x + 6 =0

Answer 2

Hi friend
formula to form quadratic equation = k(x²-Sx+P)
where K= any constant
S= sum of zeros
P = product of zeros
and sum of zeros$\frac{3- \sqrt{3} }{5} + \frac{3+ \sqrt{3} }{5} = \frac{6}{5}$
product of zeros=$\frac{(3- \sqrt{3})(3+ \sqrt{3}) }{5X5} = \frac{6}{25}$
so put the values of given zeros in the formula as :-
k(x²-6/5x+6/25)
let k=25
so quadratic equation becomes
25x²-30x+6=0
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