Mathematics : Relation between zeroes and coefficient of a polynomial.

Relationship between zeroes and coefficients of a linear polynomial

Today we are going to learn the relationship between "zeroes" and "coefficients" of a linear and quadratic polynomial. 

As we know that the general form of a linear polynomial is as following : 

ax + b , where a≠0, a and b are real numbers and x is a variable. 

So, from here we can say that the zero of a linear polynomial will

ax + b = 0 

ax = –b 

x = –b/a 

So, for any linear polynomial, say ax + b , the zero of polynomial will –b/a 

So, here b is a constant term where a is coefficient of x 

Hence, 

Zero of a linear polynomial = 

–(Constant term)/Coefficient of x 

Let's take some examples. 

Let consider 3x + 8 

We know that 

3x + 8 = 0 

3x = –8 

x = –8/3 

Here zero of polynomial p(x) = 3x + 8 is

–8/3

But as we proved that zero of a linear polynomial = 

–(Constant term)/Coefficient of x

So, 

Here , Constant term = 8 

Coefficient of x = 3 

So, by putting the given values in formula , we get that the zero of polynomial will 

–8/3 

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