Question

Check whether -2 and 2 are zeroes of the polynomial \[x+2\].

Answer 1

Hint: For the above question we would have to know about the zeroes of the polynomial. The zero of a polynomial can be defined as those values of x when substituted in the polynomial, making it equal to zero. In other words, we can say that the zeroes are the roots of the polynomial. Let us suppose that we have a polynomial P(x) and a is the zero of this polynomial. Then P(a) = 0. We have been asked whether -2 and 2 are zeroes of the above polynomial. So, we have to check if each one makes the value of the polynomial equal to zero or not.

Complete step-by-step answer:
 We know that if we have a polynomial P(x) and \[\alpha \] and \[\beta \] are the zeroes of the polynomial. Then,
\[\begin{align}
  & P\left( \alpha \right)=0 \\
 & P\left( \beta \right)=0 \\
\end{align}\]
So, -2 and 2 are the zeroes of the polynomial \[x+2\] then if we substitute these zeroes in the given polynomial it is equal to zero.
For the zero -2,
\[x+2=(-2)+2=0\]
Hence -2 is the zero of the polynomial.
For the zero 2,
\[x+2=(2)+2=4\ne 0\]
Hence 2 is not the zero of the polynomial.
Therefore, only -2 is the zero of the given polynomial among -2 and 2.

Note: Remember that we can find the zeros of a polynomial P(x) by equating it to zero. \[\Rightarrow P(x)=0\] Also remember that the number of zeroes of the polynomial is equal to the maximum exponent of the variable in the polynomial.