Write the coefficients of $ x^{2} $ in each of the following:
(i) $ 2+x^{2}+x $
(ii) $ 2-x^{2}+x^{3} $
(iii) $ \frac{\pi}{2} x^{2}+x $
(iv) $ \sqrt{2} x-1 $

To do :

We have to find the coefficient of $x^2$ in each of the given expressions.

Solution :

Coefficient :

A coefficient is the numerical part of a product of numbers and variables.

Therefore,

(i) \( 2+x^{2}+x \)

$x^{2}+x+2$ can be written as $1\times x^2+1\times x+2$

Here, $x^2$ is multiplied by $1$.

Therefore, the coefficient of $x^2$ in the given expression is $1$.  

(ii) \( 2-x^{2}+x^{3} \)

$x^3-x^{2}+2$ can be written as $1\times x^3-1\times x^2+2$

Here, $x^2$ is multiplied by $-1$.

Therefore, the coefficient of $x^2$ in the given expression is $-1$. 

(iii)  \( \frac{\pi}{2} x^{2}+x \)

$\frac{\pi}{2} x^{2}+x$ can be written as $\frac{\pi}{2}\times x^2+1\times x$

Here, $x^2$ is multiplied by $\frac{\pi}{2}$.

Therefore, the coefficient of $x^2$ in the given expression is $\frac{\pi}{2}$.

 (iv) \( \sqrt{2} x-1 \)

$\sqrt{2} x-1$ can be written as $0\times x^2+\sqrt{2} \times x-1$

Here, $x^2$ is multiplied by $0$.

Therefore, the coefficient of $x^2$ in the given expression is $0$. 

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Updated on: 10-Oct-2022

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