If `p , q , ra n ds` are real numbers such that `p r=2(q+s),` then show that at least one of the equations `x^2+p x+q=0` and `x^2+r x+s=0` has real roots.

Explanation

We have ` x^2+px+q=0`....(i)

` x^2+rx+s=0`....(ii)


Let D1​ and D2​ be the discriminants of equations (i) and (ii).

Then

`D1​=b^2−4ac=p^2−4q
`

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