Show that if `p,q,r` and `s` are real numbers and `pr=2(q+s)`, then atleast one of the equations `x^(2)+px+q=0` and `x^(2)+rx+s=0` has real roots.

Explanation

To show that at least one of the equations \(x^2 + px + q = 0\) and \(x^2 + rx + s = 0\) has real roots given the condition \(pr = 2(q + s)\), we can follow these steps:

### Step 1: Understand the conditions for real roots
For a quadratic equation \(ax^2 + bx + c = 0\) to have real roots, its discriminant must be non-negative. The discriminant \(D\) is given by:
\[ D = b^2 - 4ac \]

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