If 1 and ‒2 are two zeros of the polynomial (x3 ‒ 4x2 ‒ 7x + 10), find its third zero.


Let us assume f (x) = x3 – 4x2 – 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) = (x2 + x – 2) is a factor of f (x)


Now, on dividing f (x) by (x2 + x – 2) we get:



f (x) = 0


(x2 + 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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