Verify whether $2$ and $0$ are zeroes of the polynomial $x^{2}-2 x$.
Verify whether $2$ and $0$ are zeroes of the polynomial $x^{2}-2 x$.
Let $p(x)=x^{2}-2 x$
Then $p(2) = 2^2 -4 = 4 -4 = 0$
and $p(0) = 0 -0 = 0$
Hence, $2$ and $0$ are both zeroes of the polynomial $x^2 -2x.$
Let us now list our observations :
$(i)$ A zero of a polynomial need not be $0$.
$(ii)$ $0$ may be a zero of a polynomial.
$(iii)$ Every linear polynomial has one and only one zero.
$(iv)$ A polynomial can have more than one zero.
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