Question

what is the zero of a constant polynomial and why?

Answer 1

The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.

A real number k is a zero of a polynomial p(x), if p(k) = 0.

Answer 2

First of all you sholud know about What exactly a zero Is ?

Zero of a Ploynomial is simply any real number which makes the value of polynomial eqaul to zero...

For example...

Let p(x) = x + 1 be a polynomial , Lets find out the value of polynomial p(x) at different values of x as
x = 0 , 1 and -1...

At x=0 , we have p(0) = 0+1 = 1
=> this means value of a polynomial at x=0 is 1

At x=1 , we get p(1) = 1 + 1 = 2
and
At x= -1 , we have p(-1) = (-1) + 1 = -1 + 1 = 0

Here you can see The value of polynomial at x = -1 is 0
i.e, at x =-1 , p(x) =0
=> x = -1 or -1 is the zero of a ploynomial ( -1 is a real number here )....

Degree is the Highest power of variable in a Polynomial...
Degree classified polynomials...as

Degree = 1 is a Linear Polynomial and have only 1 zero
Degree = 2 is a quadratic Poly. and have 2 zeros
Degree = 3 is a cubic Poly. and have 3 zeros
Degree = 4 is a biQuadratic and have 4 zeros and so on...

For Constant Polynomial , Degree is 0...No zeros...
If we draw a graph of any polynomial and find out the zeros using graph...we will check the intersection of graph with x-axis...

If graph intersects the x-axis at One point , then we will have only one zero...and graph will be a straight line...
If we draw a graph of quadratic polynomial , it either touches the X-axis or intersects the x-axis at two different Points...So quadratic Poly. have two zeros....

But if we draw a graph of Constant polynomial , it ia straight line parallet to X - axis....and you will find that there is no intersection of graph with X - axis...so No zero will be there...see graph in snap..

Hope this help....