Question

find the values of a and b if x⁴-8x³+ax²+bx+16 is a perfect square​

Answer 1

Answer:

x  

4

−8x  

3

+ax  

2

−bx+16=0

α  

1

​  

+α  

2

​  

+α  

3

​  

+α  

4

​  

=8

α  

1

​  

α  

2

​  

α  

3

​  

α  

4

​  

=16

AM=GM=2

Dividing from AM−GM inequality  

(  

n

∑  

1

n

​  

i=1

​  

≥(∏  

i=1

n

​  

ai)  

1/n

)

Only when all the terms are equal .

Hence all roots are equal  

So α  

1

​  

=α  

2

​  

=α  

3

​  

=α  

4

​  

=2

So, A and B are true

Step-by-step explanation:

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