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Find the zero of the polynomial $p(x) = 3x - 2$
A. $\dfrac{1}{2}$
B. $\dfrac{3}{2}$
C. $ - \dfrac{3}{2}$
D. $\dfrac{2}{3}$

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Last updated date: 20th Jun 2024
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Answer
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Hint: Here we must know what the zero of the polynomial is. Zero of the polynomial means the value at which the given polynomial becomes zero. That value represents the zero of the polynomial. For example: If we have the polynomial $p(x) = 3x + 3$
Then we need to find the zero of this polynomial. So actually we need to find the value of $x$ at which the given polynomial is zero. So if we equate it to zero we will get
$
\Rightarrow 3x + 3 = 0 \\
\Rightarrow 3x = - 3 \\
\Rightarrow x = - 1 \\
 $
So we get that $x = - 1$ is the zero of the given polynomial.

Complete step-by-step answer:
Here we are given to find the zero of the polynomial $p(x) = 3x - 2$
So we actually need to find the value at which the given polynomial becomes zero. For example: If we have the polynomial $p(x) = 3x + 3$
Then we need to find the zero of this polynomial. So actually we need to find the value of $x$ at which the given polynomial is zero. So if we equate it to zero we will get
$
\Rightarrow 3x + 3 = 0 \\
\Rightarrow 3x = - 3 \\
\Rightarrow x = - 1 \\
 $
If we put $x = - 1$ in the given polynomial we will get $3x + 3 = 3( - 1) + 3 = - 3 + 3 = 0$
Hence we can say it is the zero of this polynomial.
Now we need to find the zero of the polynomial which is given as
$p(x) = 3x - 2$
So we need to equate it to zero and hence we will get that
$
  p(x) = 3x - 2 = 0 \\
\Rightarrow 3x - 2 = 0 \\
\Rightarrow 3x = 2 \\
 $
$\Rightarrow$ $x = \dfrac{2}{3}$
Hence we can say that when the value of the $x = \dfrac{2}{3}$ then the value of the given polynomial function is zero and therefore it is known as the zero of the given polynomial.
Hence D is the correct result.

Note: In order to solve such problems we must know what the zero of the polynomial is and how it is calculated. We simply need to equate the given polynomial to zero and get the value of the variable at which it is zero. It will be the zero of the given polynomial.