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  • A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were the answers given by the students : <img alt="\dpi{100} \fn_jvn \small 2x + 3 , 3 x^{2}+7x+2 , 4x^{3} +3x^{

A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were the answers given by the students :

\dpi{100} \fn_jvn \small 2x + 3 , 3 x^{2}+7x+2 , 4x^{3} +3x^{2} + 2 , x^{3} + \sqrt{3x} + 7 , 7x+\sqrt{7}, 5x^{3}-7x +2 , 2x^{2}+3-\frac{5}{x}, 5x - \frac{1}{2}, ax^{3}+bx^{2}+d, x+\frac{1}{x}.

Answer the following questions : (i) How many of the above ten, are not polynomials ? (ii) How many of the above ten, are quadratic polynomials ?

 

 
 
 
 
 

Answers (1)

All the exponents in the algebraic expression must be non-negative integers for the algebraic expression to be a polynomial.

$ (i)Not polynomial $ \\\\ \begin{array}{l} \text { 1) } x^{3}+\sqrt{3 x}+7 \\ \text { (2) } 2 x^{2}+3-\frac{5}{x} \\ \text { (3) } x+\frac{1}{x} \end{array} \\\\ $ (ii)Quadratic Polynomial$ \\\\ 3x^2 + 7x + 2

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Safeer PP

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