Given:
The polynomial is:
[tex]P(x)=ax+b[/tex]
To find:
Whether [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial or not.
Solution:
We have,
[tex]P(x)=ax+b[/tex]
Putting [tex]x=-\dfrac{b}{a}[/tex], we get
[tex]P(-\dfrac{b}{a})=a(-\dfrac{b}{a})+b[/tex]
[tex]P(-\dfrac{b}{a})=-b+b[/tex]
[tex]P(-\dfrac{b}{a})=0[/tex]
Since the value of the given polynomial is 0 at [tex]x=-\dfrac{b}{a}[/tex], therefore [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial.
