Question

For the quadratic equation whose roots are sum of the squares and difference of the square of the

equation

2x + 2(p + q)x + p + q = 0
​

Answer 1

Step-by-step explanation:

Let's assume roots are m and n .

So, we want the equation whose roots would be (m+n)2and(m−n)2

So, the sum of the roots(S) of our desired equation would be 2(m2+n2) and product of the roots(P) would be (m+n)2(m−n)2 .

What we know from given equation are:

m+n=−(p+q)

And

mn=(p2+q2)/2

The Sum and Product are :

S=2(m2+n2)=2(m+n)2−2mn

=2(p+q)2−(p2+q2)=2∗2pq=4pq

And

P=(m+n)2(m−n)2=(p+q)2(m+n)2−4mn

=(p+q)2(p+q)2−2(p2+q2

=(p+q)2(2pq−p2−q2)

=−(p+q)2(p−q)2

=−(p2−q2)2

Our desired equation would be x2−Sx+P=0

So, x2−4pqx−(p2−q2)2=0 is our required equatio