Write the coefficients of `x^(2)` in each of the following :
(i) `2+x^(2)+x`
(ii) `2-x^(2)+x^(3)`
(iii) `(pi)/(2)x^(2)+x`
(iv) `sqrt(2)x-1`

Answer

To find the coefficients of \( x^2 \) in each of the given expressions, we will identify the term that contains \( x^2 \) and then extract its coefficient. Let's solve each part step by step.

### Solution:

(i) **Expression:** \( 2 + x^2 + x \)

- The term containing \( x^2 \) is \( x^2 \).
- The coefficient of \( x^2 \) is **1**.

(ii) **Expression:** \( 2 - x^2 + x^3 \)

- The term containing \( x^2 \) is \( -x^2 \).
- The coefficient of \( x^2 \) is **-1**.

(iii) **Expression:** \( \frac{\pi}{2} x^2 + x \)

- The term containing \( x^2 \) is \( \frac{\pi}{2} x^2 \).
- The coefficient of \( x^2 \) is **\(\frac{\pi}{2}\)**.

(iv) **Expression:** \( \sqrt{2}x - 1 \)

- There is no term containing \( x^2 \) in this expression.
- Therefore, we consider it as \( 0x^2 \) and the coefficient of \( x^2 \) is **0**.

### Summary of Coefficients:
- (i) Coefficient of \( x^2 \) is **1**.
- (ii) Coefficient of \( x^2 \) is **-1**.
- (iii) Coefficient of \( x^2 \) is **\(\frac{\pi}{2}\)**.
- (iv) Coefficient of \( x^2 \) is **0**.