Question

Is √2x - 1 a polynomial? If yes, why?​

Answer 1

Answer:

yes because X is not in root or in denominator

Answer 2

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Question :-}}}}}}$

Is √2x - 1 is a polynomial ?

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Answer :-}}}}}}$

Yes , √2x - 1 is a polynomial.

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Explaination :-}}}}}}$

• Polynomials are algebraic expressions that consist of variables and coefficients.

• The variable of the algebraic term is raised to a whole.

• The power of a variable can be :-

(i) Positive Number

Example : p(x) = 8x² + 19

(ii) Zero

Example : g(x) = 7 [It can also be written as 7x⁰] [a⁰ = 1]

7x⁰ = 7 × x⁰ = 7 × 1 = 7

★ Polynomial with power zero is called Constant Polynomial.

• The power of variable cannot be :-

(i) Fractional number

Example : p(x) = $6x^{\frac{1}{2}}$ is not a polynomial.

(ii) Negative number

Example : g(x) = 6x⁻² is not a polynomial.

Now coming to your question.

In √2x - 1 the power of x is 1 so √2x - 1 is a polynomial.

I think your confused cause the power of 2 is ½ [√ = ½] so I would like to tell that the constant term can have Fractional or Negative power. It won't affect the polynomial. The note worthy thing is that the power of variable should be Whole Number ie. either Positive Number or Zero.

☞ Natural Numbers = Positive Numbers

☞ Whole Numbers = Zero + Positive Number

☞ Integers =  Zero + Positive Numbers + Negative Numbers

☞ Rational Numbers = Zero + Positive Numbers + Negative Numbers + Fractional Numbers

☞ Natural Numbers = Positive Number

☞ Whole Numbers = Natural Numbers + Zero

☞ Integers =  Whole Numbers + Negative Numbers

☞ Rational Numbers = Integers + Fractional Numbers