Q10 of 87 Page 53

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation

2x2 + 2(p + q)x + p2 + q2 = 0

Let’s assume roots are m and n.

So, we want the equation whose roots would be


So, the sum of the roots of our desired equation would be and product of the roots would be


What we know from given equation are:



and


the sum and product are:




and








Our desired equation would be


So, x2 - 4pqx - (p2 - q2)2 = 0 is our desired equation


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