Zero of a Linear Polynomial

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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