1
Question
If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+10, then the third zero is
If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+10, then the third zero is
Open in App
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).
Suggest Corrections
1
Similar questions