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Question

If 1 and -2 are two zeroes of the polynomial x34x27x+10, find its third zero.

A
1
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B
5
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C
- 5
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D
- 1
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Solution

The correct option is B 5
If a and b are zeroes of a polynomial f(x), then (x - a)(x - b) is a factor of f(x).
Thus, in the given problem, (x1)(x+2) is a factor of f(x)=x34x27x+10,i.e.,
(x2+x2) is a factor of f(x)=x34x27x+10.
The third zero of f(x) can be obtained by dividing f(x) by (x2+x2).

Thus, (x - 5) is also a factor of f(x).
5 is the third zero of f(x).

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