Question

α,β,γ are zeroes of cubic polynomial x^3- 12x^2+44x+c .If 2β=α+γ. Find the value of c

Answer 1

Answer:

-48

Step-by-step explanation:

α,β and  γ are zeros of cubic polynomial and are in AP.

So, Let β=a ; α=a−d & γ=a+d

Polynomial=x  

3

−12x  

2

+44x+c

Sum of roots=  

1

−(−12)

​  

=12

So,a−d+a+a+d=12

3a=12

a=4

Sum of products of two consecutive roots=44.

a(a−d)+a(a+d)+(a−d)(a+d)=44

a  

2

−ad+a  

2

+ad+a  

2

−d  

2

=44

3a  

2

−d  

2

=44

3(4)  

2

−d  

2

=44

d  

2

=48−44=4

d=±2

So, α=a−d=  

4+2

4−2

​  

=  

6

2

​  

 

β=4

β=a+d=  

4−2

4+2

​  

=  

2

6

​  

 

So,Product (−c)=2×4×6

=−48