Q. 11 C5.0( 5 Votes )

Which of the followings is a linear polynomial?
A. x + x2

B. x + 1

C. 5x2 – x + 3

D.

Answer :

For option (a),


We have x + x2


In this expression, we have 2 terms.


The degree of this expression is 2 (largest exponent of x).


But linear polynomial has a degree of 1, so that it can give exactly one root.


x + x2 is not a linear polynomial.


For option (b),


We have x + 1


In this expression, we have 2 terms.


And the degree of this expression is 1 (largest exponent of x).


This compliments the definition of a polynomial.


x + 1 is a linear polynomial.


For option (c),


We have 5x2 – x + 3.


In this expression, we have 3 terms.


And the degree of this expression is 2 (largest exponent of x).


This violates the definition of linear polynomial, as the degree of linear polynomial is always 1.


5x2 – x + 3 is not a linear polynomial.


For option (d),


We have


Let us simplify the expression.



x2 = 1


x2 – 1 = 0


This now is an algebraic expression, having 2 terms.


The degree of this expression is 2 (largest exponent of x).


This again doesn’t satisfy the criteria of linear polynomial, which says that degree should be 1.


is not a linear polynomial.


Thus, option (b) is correct.

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