Question 1175934
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This statement is ALWAYS true.


<pre>
    There are INFINITELY MANY polynomials of the form


        p(x) = r*(x-a)*(x-b)*(x-c)


    with the given zeros "a", "b" and "c", where  the coefficient "r" is any real number not equal to zero.
</pre>


It is one example of the infinite family of polynomials with the assigned property.


<pre>
    Also, there are INFINITELY MANY polynomials of the form


        p(x) = {{{(x-a)^m*(x-b)^n*(x-c)^k}}}


    with the leading coefficient of 1 with the given zeros "a", "b" and "c", 
    where  the degree indexes n, m, k are arbitrary positive integer numbers.
</pre>

It is another example.


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Solved, answered and explained.