Question

if alpha and beta are the zeroes of the polynomial x^2+6x+9 then find a polynomial whose zeroes are minus alpha and minus beta

Answer 1

the zeroes of p(x)=x^2+6x+9 are :
x^2+(3+3)x+9
=x^2+3x+3x+9
=x(x+3)+3(x+3)
=(x+3)(x+3)

So the zeroes are -3 and -3.
So alpha=-3
beta=-3
Then minus alpha=3
minus beta=3
new polynomial= x^2-( sum of zeroes) x+product of zeroes.
so your ans is x^2-6x+9