Question

Find a zero of the polynomial, \[P(x)=2x+1\].

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 to find the zero of the above polynomial. So, we have to equate it to zero and then find the zero of the polynomial.

Complete step-by-step answer:
 We have been given the polynomial \[P(x)=2x+1\].
We know that if we have a polynomial P(x) then its zeroes are given by as follows:
Equating the polynomial to zero, we will get the zeroes of the polynomial.
So the zeroes of the polynomial P(x) is \[P(x)=0\].
\[\Rightarrow 2x+1=0\]
On taking 1 to the right hand side, we get as follows:
\[\Rightarrow 2x=-1\]
On dividing the equation by 2, we get as follows:
\[\begin{align}
  & \Rightarrow \dfrac{2x}{2}=\dfrac{-1}{2} \\
 & \Rightarrow x=\dfrac{-1}{2} \\
\end{align}\]
Therefore, the zero of the given polynomial P(x) is equal to \[\dfrac{-1}{2}\].

Note: Be careful while solving the equations and take care of the sign while taking the terms to the right hand side. Also 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.