# 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 $0$.

Updated on: 10-Oct-2022

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