Question

Form the quadratic equation whose roots are the squares of the sum of roots and square of the difference of roots of the equation 2x2 +2(m + n)x + m2 +n2 = 0​

Answer 1

Answer:

Let the roots of the required equation be M and N

let the roots of the equation 2x²+2(p+q)x+p²+q²=0 be a and b

⇒a+b=−(p+q)

⇒ab=

2

(p

2

+q

2

)

⇒(a+b)

2

=(p+q)

2

⇒(a−b)

2

=(a+b)

2

−4ab

⇒(a−b)

2

=−(p−q)

2

we wanted the values of square of sum of the roots and square of difference of the roots

Now⇒M=(a+b)

2

=(p+q)

2

and

⇒N=(a−b)

2

=−(p−q)

2

⇒M+N=4pq

⇒MN=(p+q)

2

[−(p−q)

2

]

⇒MN=−(p

2

−q

2

)

2

hence the required equation is

⇒x

2

−(4pq)x−(p

2

−q

2

)

2

=0