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# Verify whether the following are zeroes of the following polynomial, indicated against them.$p\left( x \right) = 3x + 1,x = - \dfrac{1}{3}$

Last updated date: 13th Sep 2024
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Hint: The zero of the polynomial is that number which when substituted in the polynomial gives 0 . Thus, to check whether the given number is the zero of the polynomial, substitute $x = - \dfrac{1}{3}$ in the given polynomial. If the result is 0, then the answer is yes otherwise not a 0 of the polynomial.

We are given that the polynomial is $p\left( x \right) = 3x + 1$.
In the given polynomial $p\left( x \right) = 3x + 1$, the highest power that the variable is raised to is 1. Therefore, the degree of the given polynomial is 1.
We want to find out whether $x = - \dfrac{1}{3}$ is the zero of the given polynomial or not.
Now, we will substitute $x = - \dfrac{1}{3}$ in the polynomial $p\left( x \right) = 3x + 1$
$p\left( { - \dfrac{1}{3}} \right) = 3\left( { - \dfrac{1}{3}} \right) + 1 \\ p\left( { - \dfrac{1}{3}} \right) = - 1 + 1 \\ p\left( { - \dfrac{1}{3}} \right) = 0 \\$
From the above result we can conclude that $x = - \dfrac{1}{3}$ is the zero of the polynomial.