Q2 of 113 Page 61

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)


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