Question

If p(x) is a polynomial of degree 3 with leading coefficient
1006. Also p(1)=1,p(2)=3, p(3)=5. What is the value of
p(5):
O
9
( )
24153
( )
11
( )
24109​

Answer 1

Given :  p(x) is a polynomial of degree 3 with leading coefficient 1006. Also p(1)=1, p(2)=3, p(3)=5

To find : value of  P(5)

Solution:

p(x) = 1006x³  + bx² + cx  + d

P(1) =  1006   + b  + c   + d = 1

=> b  + c   + d =  -1005

P(2) =  1006*8   + 4b  + 2c   + d = 3

=> 4b  + 2c   + d =  -8045

P(3) =  1006*27   + 9b  + 3c   + d = 5

=> 9b  + 3c   + d =  -27157

3b + c  = -7040

5b + c  =  -19112

=>2b  =  -12072

=> b  =  -6036

c = 11068

d  =  -6037

p(x) = 1006x³   -6036 x² + 11068x   -6037

=> p(5)  =  24153

24153 is the correct answer

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