Which of the following is not a polynomial ? a) root 2 b) x c)1/x d) root 3x+ 5​

Question

Which of the following is not a polynomial ?
a) root 2
b) x
c)1/x
d) root 3x+ 5​

in progress 0
Sophia 2 weeks 2021-09-09T17:37:15+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-09T17:38:33+00:00

    \displaystyle\huge\red{\underline{\underline{Solution}}}

    TO CHECK

    Which of the following is not a polynomial

     \sf{a)  \:  \:  \: \sqrt{2} }

     \sf{b) \:  \: x}

     \displaystyle \sf{ c) \:  \:  \:  \frac{1}{x} \: }

     \sf{ d) \:  \:  \sqrt{3} x + 5\: }

    CONCEPT TO BE IMPLEMENTED

    POLYNOMIAL

    Polynomial is a mathematical expression consisting of constants, variables and exponents, that can be combined using addition, subtraction, multiplication

    PROCESS TO CHECK FOR POLYNOMIAL

    Polynomials have no variables in denominators or exponents, no roots of variables, and all variables have whole number exponents

    DEGREE OF A POLYNOMIAL

    Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

    When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

    CALCULATION

    CHECKING FOR OPTION ( a )

     \sf{ Here \:  \sqrt{2}   \:  \: is \:  a \:  constant \:  where \:  no \:  variable \:  is \:  present \: }

     \sf{Hence \:  \sqrt{2} \:  \:   is \:  a \:  polynomial }

    CHECKING FOR OPTION ( b )

    In this algebraic expression variable is x and the exponent is a whole number

     \sf{Hence \: \:   x \:  \:   is \:  a \:  polynomial }

    CHECKING FOR OPTION (c)

    Here

     \displaystyle \sf{ \frac{1}{x} \:  =  {x}^{ - 1} }

    So in this algebraic expression variable is x and exponent is not a whole number

     \displaystyle \sf{Hence\:  \:  \:  \frac{1}{x}  \:  \: is \: not \: a \: polyomial\: }

    CHECKING FOR OPTION (d)

     \sf{ Here \:  \:  \:  \:  \sqrt{3} x + 5\: }

    is an algebraic expression where variable is x and the exponent is a whole number

     \sf{Hence \:  \:  \:   \sqrt{3} x + 5\: } \:  \: is \: a \: polynomial

    RESULT

      \boxed{\displaystyle \sf{ \:  \: (c) \:  \: \:  \:  \:  \frac{1}{x}   \:  \: \:  \: is \: not \: a \: polyomial\:  \:  \:  \: }}

    ━━━━━━━━━━━━━━━━

    LEARN MORE FROM BRAINLY

    Show that the square of any positive integer can’t be of the form 5m+2or 5m+3 where ‘m’ is a whole number

    https://brainly.in/question/21953105

    0
    2021-09-09T17:39:14+00:00

    Answer:

    b. x is not a polynomial

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