Question

if α and β are the zeros of the polynomial x^2+6x+9, then find the polynomial whose zeros are -α and -β.

Answer 1

Answer:

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