Question

Let px be a cubic polynomial such that the coefficient of x^3 is 1.P(1)=1,p(2)=2,p(3)=3.Find p(4)

Answer 1

Answer:

Step-by-step explanation:

Let the cubic polynomial=x^3+ax^2+bx+c=0

P(1)=1

1+a+b+c=1

a+b+c=0…..(1)

P(2)=2

8+4a+2b+c=2

4a+2b+c=-6……(2)

P(3)=3

27+9a+3b+c=3

9a+3b+c=-24……(3)

(2)-(1)

3a+b=-6…..…(4)

(3)-(1)

8a+2b=-24

4a+b=-12………(5)

(5)-(4)

a=-6

b=12

c=-6

Therefore the polynomial=x^3–6x^2+12x-6=0

P(4)=64–96+48–6=112–102=10