How do you write a polynomial function of least degree given the zeros -5, $sqrt3$ ?

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Answer 1 · 2016-10-05T10:24:44

$f(x) = x^(2) - (sqrt(3) - 5) x - 5 sqrt(3)$

Let's express the function as $f(x) = (x + 5) (x - sqrt(3))$ :

$=> f(x) = (x + 5) (x - sqrt(3))$

$=> f(x) = (x) (x) + (x) (- sqrt(3)) + (5) (x) + (5) (- sqrt(3))$

$=> f(x) = x^(2) - sqrt(3) x + 5 x - 5 sqrt(3)$

$=> f(x) = x^(2) - (sqrt(3) - 5) x - 5 sqrt(3)$

How do you write a polynomial function of least degree given the zeros -5, sqrt3sqrt3?