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Question
Find the zeros of the polynomial x2 + x – p(p + 1).
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Solution
f(x) = x2 + x – p(p + 1)
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 + 1) or x = p
So, the zeroes of f(x) are – (p + 1) and p.
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