Q3 of 113 Page 61

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

We have,

f (x) = x2 – 3x – m (m + 3)


Now, by adding and subtracting px, 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


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


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