Question

Check whether the zero of the polynomial is always zero.
A. True
B. False
C. Cannot be determined
D. None of the above

Answer 1

Hint: Let us assume any polynomial and check whether the zero of
that polynomial is zero or not by putting the value of the polynomial equal to zero.

Complete step-by-step answer:
As we know that all functions that have variables are known as
polynomial functions. Polynomial function are the functions that can have any
natural number as highest degree of the variable.
And the degree of the polynomial equation is the highest power of the variable.
Now to check whether the zero of a polynomial is always zero or not.
First, we assume a polynomial and then put the value of that polynomial equal to zero. And find the value of the variable by solving that equation.
And if the value of that variable is not equal to zero, then the above given statement that zero of the polynomial is always zero will be stated as false.
So, let the polynomial f(x) be 2x + 1.
So, f(x) = 2x + 1
Now putting f(x) = 0. So, above equation becomes,
0 = 2x + 1
Subtracting 1 from both the sides of the above equation. We get,
-1 = 2x
On dividing both sides of the above equation by 2. We get,
x = \[\dfrac{{ - 1}}{2}\]
Now we can see from the above equation that zero of the polynomial f(x) is not zero.
So, from this we conclude that zero of the polynomial may or may not be equal to zero. But zero of the polynomial is not always equal to zero.
So, the given statement will be false.
Hence, the correct option will be B.

Note: Whenever we come up with this type of the problem then first, we had to take any random polynomial equation with any natural number as its highest degree and put that polynomial equation equal to zero and then find the value of the variable of that polynomial equation by solving that equation after that we check whether the value of the variable is equal to zero or not. If the value of the variable is not equal to zero then the given statement will be false.