Question 1137491
<br>
find a polynomial of degree 4 with 1 as a zero of multiplicity 2 and -3 and 5 as zeroes of multiplicity 1<br>
A zero at x=a means a factor of (x-a) in the polynomial function.  If the root is of multiplicity n, then the factor (x-a) is to the n-th power.<br>
So the polynomial in this example is<br>
{{{f(x) = (x-1)^2(x+3)(x-5)}}}<br>
Expand if required....<br>
{{{graph(400,400,-5,10,-100,60,(x-1)^2(x+3)(x-5))}}}