# Zero of a Linear Polynomial

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As we know, a linear polynomial is of the following form:

\[p\left( x \right):ax + b,\,\,a \ne 0\]

There is *only one zero* of this polynomial, and it is easy to find out that zero. We simply equate this polynomial to 0 and find out the corresponding value of *x*:

\[\begin{align} & ax + b = 0\\ \Rightarrow \;\;\;\;\;\; & x = - \frac{b}{a}\end{align}\]

Note that *a* must not be equal to 0, otherwise this zero will have an undefined value (in fact, if *a* is equal to 0, then the original polynomial will not even be linear). Here are some examples:

Liner polynomial |
Zero |

\(x+2\) | \(-\frac72\) |

\(\pi\;x-3\) | \(\frac3\pi\) |

\(\sqrt{2\;}x+4\) | \(-\frac4{\sqrt2}\) |

\(-\sqrt[{}]3x+7\) | \(\frac7{\sqrt3}\) |

## How many zero's does a linear polynomial have?

**Linear Polynomials**have only 1 zero, whereas quadratic and cubic polynomials have 2 and 3 zeroes respectively.

## How do you find the zeros of a polynomial step by step?

- To find the
**zeros of a polynomial**follow these steps (uses Rational Root Test) - Step 1: Find factors of the leading coefficient.
- Step 2: Find factors of the constant.
- Step 3: Find all the POSSIBLE rational zeros or roots.
- Step 1: Find factors of the leading coefficient.
- Step 2: Find factor of the constant.
- Step 3: Find all the possible rational zeros or roots.

## What is the zero of a linear polynomial?

- In order to find the
**zero of a linear polynomial**equate P(x)= 0. Therefore the zero of a linear polynomial ax+b is -b/a

## What makes a polynomial linear?

- any
**polynomial**that can be defined by an equation of the form. p(x) = ax + b. where a and b are real numbers and a (not equal to sign) 0 is considered to be linear. For example, p(x)=3x-7

## Is Pi a polynomial?

- Since a
**polynomial**refers to an equation that has four or more variables, Pi (π) cannot be considered as a polynomial. It is only a value referring to the circumference of a circle.

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