We are asked:

Given , consider the quadratic:

Find the nature of its roots.

Step 1: Simplify using

From

Coefficient of

Coefficient of

Constant term:

So quadratic becomes:

(after dividing by -2 )

Step 2: Nature of roots

Original coefficients rational

So quadratic has rational coefficients

Roots may be rational or irrational depending on discriminant.

But nothing is specified about , so in general, roots can be rational.

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