Question

Find the zeroes of the following polynomial: \[p(x) = x - 2\]

Answer 1

Hint:
We will use the definition of the zeros of polynomials. We will equate the given polynomial to zero and simplify further to find the value of \[x\]. A polynomial is defined as an expression which is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division.

Formula used:
If \[x\] is a zero of a polynomial, then \[p(x) = 0\].

Complete step by step solution:
The given polynomial is \[x - 2\]. This is a polynomial in \[x\] or here \[x\] is the variable and 2 is the constant.
\[p(x) = x - 2\] ……….\[\left( 1 \right)\]
Now, a zero of a polynomial is that value of \[x\] for which the polynomial vanishes i.e., \[p(x) = 0\].
So, to get the zero of the given polynomial, we have to put \[p(x) = 0\]. From this, we have to find the value of \[x\].
In equation \[\left( 1 \right)\], let us put \[p(x) = 0\]. Therefore, we get
\[0 = x - 2\]
Adding 2 on both the sides, we get
\[ \Rightarrow 0 + 2 = x - 2 + 2\]
\[ \Rightarrow x = 2\]

Hence, the zero of the polynomial \[p(x) = x - 2\], i.e., the value for which \[p(x)\] vanishes, is \[x = 2\].

Note:
The number of zeroes of a polynomial depends on the degree of the polynomial. The degree of a polynomial is the highest power of the variable in a polynomial equation. The polynomial given to us is a linear polynomial. This means that the highest power of \[x\] in the polynomial is 1. Thus, there is at most 1 zero of the polynomial. Similarly, in a quadratic polynomial, the highest degree is 2, so the zeros of the polynomial are 2.