Question

In polynomial p(x)=ax^2+bx+c, p(0)=12 , p(1)=6 , p(2)=2 . Find p(3) and p(4)​

Answer 1

Answer:

P(x) = ax^2 + bx + c. P(0)= a(0) + b(0) + c = 1. = > c=1. P(1) = a(1 *1) + b(1) + 1 = 6. => a+b=5 ——— A. P(-1)= a(-1 * -1) + b(-1) + 1 =2.

Answer 2

Answer:

p(x)=ax  

2

+bx+8

p(2)=6

4a+2b+8=6

4a+2b=−2

The minimum value of p(x) occurs when

x=  

2a

−b

​  

 

∴2=  

2a

−b

​  

 

    4a+b=0

    4a+2b=−2

(−)   (−)

________________

−b=−2

b=2

4a+2=0

a=  

4

−2

​  

=  

2

−1

​  

 

a=  

2

−1

​  

 

b=2.