If 1 and ‒2 are two zeros of the polynomial (x^{3} ‒ 4x^{2} ‒ 7x + 10), find its third zero.

Let us assume f (x) = x^{3} – 4x^{2} – 7x + 10

As 1 and – 2 are the zeros of the given polynomial therefore each one of (x – 1) and (x + 2) is a factor of f (x)

Consequently, (x – 1) (x + 2) = (x^{2} + x – 2) is a factor of f (x)

Now, on dividing f (x) by (x^{2} + x – 2) we get:

f (x) = 0

(x^{2} + x – 2) (x – 5) = 0

(x – 1) (x + 2) (x – 5) = 0

∴ x = 1 or x = - 2 or x = 5

Hence, the third zero is 5

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