if α and β are the zeros of the polynomial x^2+6x+9, then find the polynomial whose zeros are -α and -β.
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sum of zero alpha + beta= -6
product of zeroes alpha × beta =9
sum of zeroes of the polynomial that we have to find
here I will use alpha as a and beta as b
a+b=-a-b
taking minus common -(a+b)
-(-6)
=6
product of zeroes are (-a)(-b)
-(a×b)
= -9
there fore the polynomial = x^ -sx +p
x^2-6x-9
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