Find the zeros of the polynomial x2 + x ‒ p (p + 1).
We have,
f (x) = x2 + x – p (p + 1)
Now, by adding and subtracting px, we get
f (x) = x2 + px + x – px – p (p + 1)
= x2 + (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)