Question

10. Find quadratic equation such that its roots are square of sum of the roots and
square
of difference of the roots of equation 2x^2+2 (p+q)x+p^2+q^2= 0








please give me answer urgent ​

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