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Question
Find the zeros of the polynomial x2 – 3x – m(m + 3).
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Solution
f(x) = x2 – 3x – m(m + 3)
By adding and subtracting mx, we get
f(x) = x2 – 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
So, the zeroes of f(x) are –m and +3.
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