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How to find the roots of given equation to find the value of p and q ?

How to find the roots of given equation to find the value of p and q ?

Grade:12

1 Answers

Priyanshu Gujjar
101 Points
one month ago

 

We know that if p and q are the roots of a quadratic equation ax2+bx+c=0, the sum of the roots is p+q=ab and the product of the roots is pq=ac.
 
Here, the given quadratic equation 2a24a+1=0 is in the form ax2+bx+c=0where a=2,b=4 and c=1.
  
The sum of the roots is:
 
p+q=ab=2(4)=2
 
The product of the roots is ac that is:
 
pq=ac=21 
 
Now, 
 
(p+q)2+4pq=22+(4×21)=4+2=6  
  
Hence, the value of (p+q)2+4pq=6.

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