Verify whether the indicated numbers are zeros of the polynomials corr

1.	Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:(i) f(x) = x2, x=0(ii) f(x) =1x + m, x= \(-\frac{m}{1}\)(iii) f(x) = 2x + 1, x = \(\frac{1}{2}\)
Answer» (i) f (x) = x² Put x = 0 Therefore, x = 0 is not a root of f (x) = x² (ii) f (x) = lx + m Put x = \(\frac{-m}{i}\) f\((\frac{-m}{i})=\) l x \((\frac{-m}{i})\) + m = - m + m = 0 = 0 Therefore, x = \(-\frac{-m}{i}\) is a root of f (x) = lx + m (iii) f (x) = 2x + 1 Put x = \(\frac{1}{2}\) f\((\frac{1}{2})\) = 2 x \(\frac{1}{2}+1\) = 1 + 1 = 2 \(\neq0\) Therefore, x = \(\frac{1}{2}\) is not a root of f (x) = 2x + 1

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:(i) f(x) = x2, x=0(ii) f(x) =1x + m, x= \(-\frac{m}{1}\)(iii) f(x) = 2x + 1, x = \(\frac{1}{2}\)

Answer»

(i) f (x) = x²

Put x

= 0

Therefore,

x = 0 is not a root of f (x) = x²

(ii) f (x) = lx + m

Put x = \(\frac{-m}{i}\)

f\((\frac{-m}{i})=\) l x \((\frac{-m}{i})\) + m

= - m + m = 0

= 0

Therefore,

x = \(-\frac{-m}{i}\) is a root of f (x) = lx + m

(iii) f (x) = 2x + 1

Put x = \(\frac{1}{2}\)

f\((\frac{1}{2})\) = 2 x \(\frac{1}{2}+1\)

= 1 + 1

= 2 \(\neq0\)

Therefore,

x = \(\frac{1}{2}\) is not a root of f (x) = 2x + 1