Question

Verify whether the following are zeroes of the polynomial, indicated against them.
\[P(x)={{x}^{2}};x=0\]

Answer 1

Hint: In this question, we have been given the zeros of the polynomial. We know that the zeroes of a polynomial can be defined as those values of x which when substituted in the equation of the polynomial make it equal to zero. Therefore, we just have to substitute x in it and check if it results in 0 or not.

Complete step-by-step answer:

We have been given the polynomial \[P(x)={{x}^{2}}\] and to verify the zero, x = 0.
Now we know that if a polynomial P(x) has zero ‘\[\alpha \]’ then if we substitute ‘\[\alpha \]’ in P(x) we get the value of the polynomial as 0.
So, according to the question, if x = 0 is the zero of the polynomial \[P(x)={{x}^{2}}\] then P(0) = 0.
\[\Rightarrow P(0)={{\left( 0 \right)}^{2}}=0\]
Hence, 0 is the zero of the polynomial.
Therefore, it is verified that x = 0 is the zero of polynomial P(x).

Note: Remember that zeroes of a polynomial are also known as roots of a polynomial. Also remember that the number of zeroes of the polynomial is equal to the maximum exponent of the variable in the polynomial So, here we have the degree of the polynomial as 2, which means that there must be 2 zeroes satisfying it. But, in this case, we have only one value possible of x, i.e. 0 which satisfies the equation of the polynomial as the square root of 0 is 0 alone and not +0 and -0.