Question

Find the zero of the polynomial $p\left( x \right)=2x+5$?

Answer 1

Hint: First we will understand the meaning of the term ‘zero of a polynomial’. Now, to find the zero of the given polynomial $p\left( x \right)$ we will substitute it equal to 0 and form a linear equation in x. Finally, we will solve this equation for the value of x to get the answer.

Complete step by step solution:
Here we have been provided with a polynomial $p\left( x \right)=2x+5$ and we are asked to find its zero. First we need to understand the meaning of the term ‘zero of a polynomial’.
Now in mathematics the term zero of a polynomial $f\left( x \right)$ means the value of the domain (x) for which we should get the value of the function $f\left( x \right)$ equal to 0. It is also called the root of the polynomial. There can be more than one root of a polynomial depending of the degree of the given polynomial. For example: - a linear equation has only one root, a quadratic equation has two roots (may be real or imaginary) and so on. If we have to find the root or zero of a polynomial we substitute the polynomial equal to 0 and solve for the value of x.
Let us come to the question. We have to find the zero of the polynomial $p\left( x \right)=2x+5$, so substituting it equal to 0 we get,
$\Rightarrow 2x+5=0$
Clearly this is a linear equation so solving for the value of x we get,
$\begin{align}
  & \Rightarrow 2x=-5 \\
 & \therefore x=\dfrac{-5}{2} \\
\end{align}$
Hence $\dfrac{-5}{2}$ is a zero of the given polynomial.

Note: We can also understand the meaning of root of zero of a polynomial graphically. In the graphical solution of a polynomial the root or zero is the point where the curve of the polynomial cut the x – axis. At this point the value of y coordinate is 0. To determine this point we solve the polynomial algebraically by substituting it equal to 0.