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Question
If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+10, find its third zero.
If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+10, find its third zero.
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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) is a factor of f(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).
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) is a factor of f(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).
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