Question

Find the zero of the polynomial in the following case:
\[P(x)=cx+d;c\ne 0\], c and d are real numbers

Answer 1

Hint: We have been given a polynomial and we have to find its zeroes. So, we must know that the zeroes of any polynomial are those values of x which when substituted in that polynomial results in the value as 0. So, we must equate the polynomial to 0 in order to find its zeroes.

Complete step-by-step answer:

We have been given the polynomial \[P(x)=cx+d;c\ne 0\], c and d are real numbers.
We know that the zeroes of a polynomial P(x) can be obtained by equating the polynomial equal to 0. So the zero of the given polynomial P(x) is as follows:
\[\begin{align}
  & P(x)=0 \\
 & \Rightarrow cx+d=0 \\
\end{align}\]
On taking d to the right-hand side we get as follows:
\[\Rightarrow cx=-d\]
On dividing the equation by c we get as follows:
\[\begin{align}
  & \Rightarrow \dfrac{cx}{c}=\dfrac{-d}{c} \\
 & \Rightarrow x=\dfrac{-d}{c} \\
\end{align}\]
Therefore, the zero of the polynomial is equal to \[\dfrac{-d}{c}\].

Note: Be careful while solving the equations and take care of the sign while taking the terms to the right- hand side. Also, we must remember that zeroes of a polynomial are also known as roots of a polynomial. Another point that we must keep in mind is that the number of zeroes of the polynomial is equal to the maximum exponent of the variable in the polynomial. So, in this question, we can have only one zero for the given polynomial.