Question

Which of the following is a polynomial?

(a) x^2+2x+5

(b) √x+2x+4

(c) x^\(\frac {2}{3}\)+10x

(d) 5x+\(\frac {5}{x}\)

I had been asked this question during an interview.

I want to ask this question from Geometrical Meaning of Zeros of Polynomial topic in chapter Polynomials of Mathematics – Class 10

Answer 1

The correct choice is (a) x^2+2x+5

To explain: An expression in the form of (x)=a0+a1x+a2x^2+…+anx^n, where an≠0, is called a polynomial where a1, a2 … an are real numbers and each power of x is a non-negative integer.

In case of √x+2x+4 , the power of √x is not an integer. Similarly for x^\(\frac {2}{3}\)+10x, \(\frac {2}{3}\) is a fraction.

Now, 5x+\(\frac {5}{x}\) in this case the power of x is a negative integer. Hence it is not a polynomial.