Let a,b,c ` in R and a gt 0`. If the quadratic equation ` ax^(2) +bx +c=0` has two real roots `alpha and beta` such that ` alpha gt -1 and beta gt 1` , then show that ` 1 + |b/a| + c/a gt 0`

Explanation

To solve the problem, we need to show that \( 1 + \left| \frac{b}{a} \right| + \frac{c}{a} > 0 \) given that the quadratic equation \( ax^2 + bx + c = 0 \) has two real roots \( \alpha \) and \( \beta \) such that \( \alpha > -1 \) and \( \beta > 1 \).

### Step-by-Step Solution:

1. **Understanding the Roots**:
Since the quadratic equation has real roots, the discriminant must be non-negative:
\[
D = b^2 - 4ac \geq 0
...