13. if 1 and -2 are two zeros of the polynomial (x ^ 3 - 4x ^ 2 - 7x + 10) find its third zero.

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If 1 and 2 are two zeroes of the polynomial x3 4x2 7x + 10, then the third zero is.

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`Let f(x) = x^3 – 4x^2 – 7x + 10` Since 1 and –2 are the zeroes of f(x), it follows that 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).

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.