Find the zeros of the polynomial x^{2} – 3x – m (m + 3).

We have,

f (x) = x^{2} – 3x – m (m + 3)

Now, by adding and subtracting px, we get

f (x) = x^{2} - mx - 3x + mx – m (m + 3)

= x [x – (m + 3)] + m [x – (m + 3)]

= [x - (m + 3)] (x + m)

∴ f (x) = 0

[x - (m + 3)] (x + m) = 0

[x - (m + 3)] = 0 or (x + m) = 0

x = m + 3 or x = - m

Hence, the zeros of the given polynomial are - m and m + 3

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