Question 1194014
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The polynomial of degree 3, P(x) has a root multiplicity 2 at x=2 and a root of multiplicity 1 at x=-5. 
The y intercept is y=-16. Find a formula for P(x)
P(x)=
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<pre>
From the "given" part,  P(x) = {{{a*(x-2)^2*(x+5)}}},  and only real coefficient "a" is unknown.


To find it, use the condition about y-intercept (which happens when x=0).  It gives


    {{{a*(-2)^2*5}}} = -16.


From this equation, find "a"

    a*4*5 = - 16

    a = {{{-4/5}}}.


Hence,  P(x) = {{{(-4/5)*(x-2)^2*(x+5)}}}.    <U>ANSWER</U>
</pre>

Solved.