Question

Consider the following statements

statement -1 The degree of a non zero constant polynomial is also a non zero.

statement -2 Every real number is a zero of a zero polynomial

Which of the following is true?

• A. Statement 1 is true and Statement 2 is false.
• B. Statement 1 is false and Statement 2 is true.
• C. both the Statements 1 and 2 are true.
• D. both the Statements 1 and 2 are false.

Answer 1

The correct option is B

Statement 1 is false and Statement 2 is true.

Explanation of statement 1:

Let us take an examples,

$f\left(x\right)=5$ , which is a non zero constant polynomial .

which can be written as $f\left(x\right)=5x^0$

Hence the degree of the polynomial $f\left(x\right)$ is zero .

Therefore, the degree of a non-zero constant polynomial is zero .

so, statement -1 is false .

Explanation of statement 2:

Also let,$g\left(x\right)=0$ which is a zero polynomial .

If we put any real number for x then its value is zero because the coefficient of the zero polynomial is also zero

for examples, $0x^2+0x+0$

$g\left(7\right)=0,g\left(5\right)=0,.......$

Hence, every real number is a zero of a zero polynomial

So, statement -2 is true

Hence, the correct answer is an option (b)