express as perfect square x⁴+2x³+3x²-2x+1

Asked by mobarakhussain70993 | 29th Aug, 2021, 08:41: AM

Expert Answer:

Let , x4 + 2 x3 + 3 x2 + 2 x + 1 = ( x2 + a x + b )2
 
RHS = x4 + a2 x2 + b2 + 2a x3 + (2ab) x + 2b x2 
 
If we compare the expanded RHS and LHS , we get , 
 
2a = 2 , i.e a = 1  
 
2ab = 2 ,  hence if a =1 , b = 1
 
Hence , we get , x4 + 2 x3 + 3 x2 + 2 x + 1 = ( x2 + x +1 )2
 
To get a perfect square of given polynomial , coefficient of x term should be +2 not -2 .
Hence the coefficient of x term is changed .
If we do not change it is not possible to express the given polynomial as perfect square

Answered by Thiyagarajan K | 17th Sep, 2021, 01:47: PM