Home
Class 9
MATHS
which of the following expressions a...

which of the following expressions are polynomials ? Justify your answer,
(i) 8 (ii) `sqrt(3x)^(2)-2x
(iii) 1-sqrt(5x)`
`(iv) (1)/(5x^(-2))+5x+7
(v) ((x-2)(x-4))/(x) (vi) (1)/(x+1)`
(vii)` (1)/(7)a^(3)-(2)/(sqrt(3))a^(2)+4a-7
(viii) (1)/(2x)`

Text Solution

AI Generated Solution

To determine which of the given expressions are polynomials, we need to understand the definition of a polynomial. A polynomial is an expression that can contain constants, variables, and non-negative integer exponents of variables. Let's analyze each expression step by step. ### Step-by-Step Solution: 1. **Expression (i): 8** - This is a constant term. It can be expressed as \(8x^0\), where the exponent of \(x\) is 0 (which is a non-negative integer). - **Conclusion**: Yes, this is a polynomial. ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • NUMBER SYSTEMS

    NCERT EXEMPLAR|Exercise SHORT ANSWER TYPE QUESTIONS|1 Videos

  • QUADRILATERALS

    NCERT EXEMPLAR|Exercise Quadrilaterals|56 Videos

Similar Questions

Explore conceptually related problems

Which of the following expressions are not polynomials? x^(2)+2x^(-2) (ii) sqrt(ax)+x^(2)-x^(3)3y^(3)-sqrt(5y)+9( iv) ax^((1)/(2))+ax+9x^(2)+43x^(-2)+2x^(-1)+4x+5

Which of the following expressions are polynomials ? In case of a polynomial write its degree. (i) x^(3)-5x+2 (ii) y^(2)+sqrt(2)y-sqrt(5) (iii) 2sqrt(x)+7 (iv) -6 (v) 4t^(2)+(1)/(6)t+2sqrt(3) (vi) z^(2)+(5)/(z^(2))+1 (vii) (1)/(3x) (viii) 1-sqrt(5x) (ix) (1)/(4x^(-2))+3x+5 (x) (6sqrt(x)+x^(3//2))/(sqrt(x))

Knowledge Check

  • Which of the following algebraic expressions are polynomials? I. x^(3) + sqrt(3x) + 4 , II. x^(2) + 2sqrt(x) + 4 III. x^(2) + sqrt(x-1) , IV. x^(2) + 3x + 4

    A
    I, II and III
    B
    Only IV
    C
    All of these
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    Solve (i) sqrt(5x^(2)-6x+8)-sqrt(5x^(2)-6x-7)=1 (ii)Solve (x^(2)-5x+7)^(2)-(x-2)(x-3)=1

    Which of the following expressions are polynomials ? In case of a polynomial , write its degree. (i) x^(5)-2x^(3)+x+sqrt(3) (ii) y^(3)+sqrt(3)y (iii) t^(2)-(2)/(5)t+sqrt(5) (iv) x^(100)-1 (v) (1)/(sqrt(2))x^(2)-sqrt(2)x+2 (vi) x^(-2)+2x^(-1)+3 (vii) 1 (viii) (-3)/(5) (ix) (x^(2))/(2)-(2)/(x^(2)) (x) root(3)(2)x^(2)-8 (xi) (1)/(2x^(2)) (xii) (1)/(sqrt(5))x^(1//2)+1 (xiii) (3)/(5)x^(2)-(7)/(3)x+9 (xiv) x^(4)-x^(3//2)+x-3 (xv) 2x^(3)+3x^(2)+sqrt(x)-1

    Which of the following are polynomials : (i) 3x^(2)-7x+6 " " (ii) x^(2)-sqrt(3)x+4 " " (iii) 3sqrt(x)+5 " " (iv) 13 " " (v) a+(5)/(a)+6

    sqrt(3x^(2)-7x-30)-sqrt(2x^(2)-7x-5)=x-5

    Which of the following are polynomials ? (i) x^(2)-3x+1 " " (ii) x^(2)+5x+2 " "(iii) x-(1)/(y) " " (iv) x^(7)+8 " " (v) x^(3)+sqrt(x)-2 (vi) sqrt(2)x^(2)+x-1 " " (vii) (3x-1)(x+5) " " (viii) (x-(3)/(x))(x+2) " " (ix)2x^(2)-1 (x) x+(1)/(sqrt(x))+2

    (i) (2x+3) (3x-5) (ii) x(1+x)^(3) (iii) (sqrtx + 1/x) (x -1/sqrtx) (iv) (x-1/x)^(2) (v) (x^(2) + 1/x^(2))^(3) (vi) (2x^(2) +5x-1) (x-3)

    Which of the following are quadratic equations? (i) x^(2)-5x+3=0 (ii) 2x^(2)-3sqrt(2)x+6=0 (iii) 3x^(2)-2sqrtx+8=0 (iv) 2x^(2)-3=0 (v) x+(1)/(x)=x^(2) (vi) x^(2)+(1)/(x^(2))=4(1)/(4)

    Home
    Profile