Find the zeros of the polynomial x2 + x ‒ p (p + 1).

1.	Find the zeros of the polynomial x2 + x ‒ p (p + 1).
Answer» Let f(x) = x² + x ‒ p (p + 1) Above polynomial can be written as, = x² + (p + 1) x – px – p (p + 1) = x (x + (p + 1)) – p (x + (p + 1)) = (x – p)(x + (p + 1)) To find the zeroes of f(x), put f(x) = 0 (x – p)(x + (p + 1)) = 0 either (x – p) = 0 or (x + (p + 1)) = 0 x = p or x = – (p + 1) Hence, the zeros of the given polynomial are p and – (p + 1)

Answer»

Let f(x) = x² + x ‒ p (p + 1)

Above polynomial can be written as,

= x² + (p + 1) x – px – p (p + 1)

= x (x + (p + 1)) – p (x + (p + 1))

= (x – p)(x + (p + 1))

To find the zeroes of f(x), put f(x) = 0

(x – p)(x + (p + 1)) = 0

either (x – p) = 0 or (x + (p + 1)) = 0

x = p or x = – (p + 1)

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

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