Question

What is the quadratic equation of the given sum and product of a square root m,n?

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

Step-by-step explanation: