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Question
Find the zeroes of the polynomial `x^2 – 3x – m(m + 3)`
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Solution
`f(x) = x^2 – 3x – m (m + 3)`
By adding and subtracting mx, 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`
So, the zeroes of f(x) are –m and +3.
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