Grade 12Algebra
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 ?
1 Answer
Priyanshu Gujjar
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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