Question

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:

(i) $f\left(x\right)=3x+1,x=-\frac{1}{3}$

(ii) $f\left(x\right)=x^2-1,x=1,-1$

(iii) $g\left(x\right)=3x^2-2,x=\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}}$

(iv) $p\left(x\right)=x^3-6x^2+11x-6,x=1,2,3$

(v) $f\left(x\right)=5x-\mathrm{\pi },\mathrm{x}=\frac{4}{5}$

(vi) $f\left(x\right)=x^2,x=0$

(vii) $f\left(x\right)=lx+m,x=-\frac{m}{1}$

(viii) $f\left(x\right)=2x+1,x=\frac{1}{2}$

Answer 1

(i) To check whether the given number is the zero of the polynomial or not we have to find

Hence, is the zeros of the given polynomial.

(ii) To check whether the given number is the zero of the polynomial or not we have to find and

Now,

And ,

Hence, and x = 1 are the zeros of the polynomial.

(iii) To check whether the given number is the zero of the polynomial or not we have to find

Now,

And

Here, both the value of , are not satisfied the polynomial. Therefore, they are not the zeros of the polynomial.

(iv) To check whether the given number is the zero of the polynomial or not we have to find

And

Hence, x = 1, 2, 3 are the zeros of the polynomial p(x).

(v)To check whether the given number is the zero of the polynomial or not we have to find

Here, , does not satisfy therefore, is not a zero of the polynomial.

(vi)To check whether the given number is the zero of the polynomial or not we have to find

Hence, x = 0 is the zeros of the polynomial.

(vii) To check whether the given number is the zero of the polynomial or not we have to find

Hence, is zeros of the polynomial.

(viii)To check whether the given number is the zero of the polynomial or not we have to find

Hence, does not satisyf the polynomial, so, is not zero of the polynomial.