Q2 of 82 Page 4

Find the zeros of the polynomial x2 + x ‒ p (p + 1).(CBSE 2011)

We have,

f (x) = x2 + x – p (p + 1)


f (x) = x2 + (p + 1 - p)x – p (p + 1)

= x2 + (p + 1) x – px – p (p + 1)

= x [x + (p + 1)] – p [x + (p + 1)]

= [x + (p + 1)] (x – p)


To find the zeroes of f(x), let 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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