For what value(s) of `lamda` the quadratic equation `x^(2)+lamdax+(lamda+1.25)=0` has :
(i) coincident roots (ii) real and distinct roots (iii) no real roots?

Explanation

To solve the problem of finding the values of \( \lambda \) for which the quadratic equation \( x^2 + \lambda x + (\lambda + 1.25) = 0 \) has coincident roots, real and distinct roots, and no real roots, we can follow these steps:

### Step 1: Identify coefficients
The given quadratic equation is:
\[ x^2 + \lambda x + (\lambda + 1.25) = 0 \]
Here, we can identify the coefficients:
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