Are the following statements 'True' or 'False'? Justify your answers.
The only value of $k$ for which the quadratic polynomial $k x^{2}+x+k$ has equal zeros is $\frac{1}{2}$.

(B) False.
Let the quadratic polynomial be $f(x) = k x^{2} + x + k$.
For the polynomial to have equal zeros,its discriminant $D$ must be equal to $0$.
The discriminant is given by $D = b^{2} - 4ac$.
Here,$a = k$,$b = 1$,and $c = k$.
Substituting these values into the discriminant formula:
$D = (1)^{2} - 4(k)(k) = 0$
$1 - 4k^{2} = 0$
$4k^{2} = 1$
$k^{2} = \frac{1}{4}$
$k = \pm \frac{1}{2}$
Therefore,there are two values of $k$,which are $\frac{1}{2}$ and $-\frac{1}{2}$,for which the quadratic polynomial has equal zeros. Thus,the statement is false.