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)
Answers
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
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Answer:
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
Step-by-step explanation: