**Question:**

Given that and are the roots of the quadratic equation , find the value of

**Solution:**

Let and be the two roots of the given quadratic equation:

By Viete’s relations between roots and coefficients:

and but we also know that

Now, let us call which in turn is same as

We have already determined in terms of p and q above.

Now, again note that which in turn gives us that so we get:

so that

Hence, the given expression E becomes:

, which is the desired solution.

🙂 🙂 🙂

Nalin Pithwa.

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