SOLUTION: Find the quadratic function whose zeroes are 1- √ 3/2 and 1+ √ 3/2 (only the 3's are under √ , not the whole fractions seen above)

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Question 1096362: Find the quadratic function whose zeroes are 1- √ 3/2 and 1+ √ 3/2
(only the 3's are under √ , not the whole fractions seen above)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are infinite answers, but I will give you one.
Quadratic functions always have "two zeros" that can be
different real numbers, or
the same real number, or
conjugate complex numbers.
Given all the zeros of a quadratic function,
there is only one quadratic function with 1 as its "leading coefficient"
and exactly those zeros.
However, multiplying that function times any non-zero number,
You get another quadratic function with exactly the same zeros.
If red%28%281-sqrt%283%29%2F2%29%29 and green%28%281%2Bsqrt%283%29%2F2%29%29 are zeros of a quadratic function,
the function can be written as
a%2A%28x-red%28%281-sqrt%283%29%2F2%29%29%29%2A%28x-green%28%281%2Bsqrt%283%29%2F2%29%29%29=a%2A%28x-1%2Bsqrt%283%29%2F2%29%2A%28x-1-sqrt%283%29%2F2%29=a%2A%28%28x-1%29%5E2-3%2F4%29=a%2A%28x%5E2-2x%2B1-3%2F4%29=a%2A%28x%5E2-2x%2B1%2F4%29
So, one solution is highlight%28f%28x%29=x%5E2-2x%2B1%2F4%29 .