Find the zeros of the polynomial x^{2} + x ‒ p (p + 1).

We have,

f (x) = x^{2} + x – p (p + 1)

Now, by adding and subtracting px, we get

f (x) = x^{2} + px + x – px – p (p + 1)

= x^{2} + (p + 1) x – px – p (p + 1)

= x [x + (p + 1)] – p [x + (p + 1)]

= [x + (p + 1)] (x – p)

∴ f (x) = 0

[x + (p + 1)] (x – p) = 0

[x + (p + 1)] = 0 or (x – p) = 0

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

Hence, the zeros of the given polynomial are p and – (p + 1)

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