Question

Find the zeroes of the polynomial x² +x-p(p+1)

Answer 1

x2+x-p(p+1)=0
x2+(p+1)x-px-p(p+1)=0

{(p+1)x-px=px+x-px=x}

Taking x and p outside,

x(x+p+1) -p(x+p+1)=0

Taking (x+p+1) outside,

(x+p+1)(x-p)=0
Hence,
x=-p-1, p