If 2a+3b+6c = 0, then show that the equation `a x^2 + bx + c = 0` has atleast one real root between 0 to 1.

Explanation

To show that the equation \( ax^2 + bx + c = 0 \) has at least one real root between 0 and 1 given that \( 2a + 3b + 6c = 0 \), we can follow these steps:

### Step 1: Define the function
Let \( f(x) = ax^2 + bx + c \). We need to evaluate \( f(x) \) at the endpoints of the interval [0, 1].

### Step 2: Calculate \( f(0) \)
Evaluate \( f(0) \):
\[
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