How do you write a polynomial function of least degree and leading coefficient $1$ $1$ when the zeros are $3, 0, - 2$ $3, 0, -2$ ?

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Answer 1 · 2016-08-06T13:06:30

$f (x) = x^{3} - x^{2} - 6 x$ $f(x) = x^3-x^2-6x$

Each zero corresponds to a linear factor, so we can define:

$f (x) = (x - 3) (x - 0) (x + 2) = x (x - 3) (x + 2) = x^{3} - x^{2} - 6 x$ $f(x) = (x-3)(x-0)(x+2)=x(x-3)(x+2)=x^3-x^2-6x$

Any polynomial in $x$ $x$ with these zeros will be a multiple (scalar or polynomial) of this $f (x)$ $f(x)$ .

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