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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 year 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 2a2−4a+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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