Question

Find the zeros of the polynomial x² – 3x – m(m + 3).

Answer 1

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.