If `t_1a n dt_2` are the ends of a focal chord of the parabola `y^2=4a x ,` then prove that the roots of the equation `t_1x^2+a x+t_2=0` are real.

Explanation

To prove that the roots of the equation \( t_1 x^2 + a x + t_2 = 0 \) are real, given that \( t_1 \) and \( t_2 \) are the ends of a focal chord of the parabola \( y^2 = 4ax \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of the focal chord**:
For the parabola \( y^2 = 4ax \), if \( t_1 \) and \( t_2 \) are the parameters corresponding to the endpoints of a focal chord, then the product of the parameters is given by:
\[
t_1 t_2 = -1
...