If the squared difference of the zeros of the quadratic polynomial f(x)=x2+px+45 is equal to 144, find the value of p.

A s space w e space k n o w comma space f o r space a space q u a d r a t i c space e q u a t i o n space
a x squared plus b x plus c equals 0
s u m space o f space r o o t s space equals space fraction numerator negative b over denominator a end fraction
P r o d u c t space o f space r o o t s space equals space c over a
alpha plus beta equals negative p
alpha beta equals 45

left parenthesis alpha minus beta right parenthesis squared equals 144
left parenthesis alpha plus beta right parenthesis squared minus 4 alpha beta equals 144
left parenthesis negative p right parenthesis squared minus 4 left parenthesis 45 right parenthesis equals 144
p squared equals 144 plus 180
p squared equals 324
p equals 18
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