If `f(x)=0` is a quadratic equation such that `f(-pi)=f(pi)=0` and `f(pi/2)=-(3pi^2)/4,` then `lim_(x->-pi)(f(x))/("sin"(sinx)` is equal to (a)`0` (b) `pi` (c) `2pi` (d) none of these

Options

A. `-(3)/(2)pi`
B. `-(1)/(2)`
C. `(2pi)`
D. `(3)/(2)pi`

Explanation

To solve the problem step by step, we start with the given information about the quadratic function \( f(x) \).

### Step 1: Determine the form of \( f(x) \)
Since \( f(-\pi) = 0 \) and \( f(\pi) = 0 \), we know that \( -\pi \) and \( \pi \) are the roots of the quadratic equation. Therefore, we can express \( f(x) \) in the form:
\[ f(x) = a(x - \pi)(x + \pi) \]
This simplifies to:
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