If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+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, (x−1)(x+2)isafactoroff(x)=x3−4x2−7x+10,i.e., (x2+x−2) is a factor of f(x)=x3−4x2−7x+10. The third zero of f(x) can be obtained by dividing f(x)by(x2+x−2).
Thus, (x - 5) is also a factor of f(x). ⇒ 5 is the third zero of f(x).