Question

let p(x) be a polynomial of degree 4 such that p(n)=120/n for n = 1,2,3,4,5 determine the value of p(6)​

Answer 1

Answer:Let P(x) be a polynomial of degree 4 such that P(n)=120n for n=1,2,3,4,5. Determine the value of P(6).

Let P(x)=ax4+bx3+cx2+dx+e. For n=1,2,3,4,5 I have plugged it into this polynomial and got the following —

P(1)=a+b+c+d+e=120

P(2)=16a+8b+4c+2d+e=60

P(3)=81a+27b+9c+3d+e=40

...

And what the problem asks for is

P(6)=1296a+216b+36c+6d+e.

However, I'm not sure if all this is helping me very much. So noticing that 2P(2)=P(1)=3P(3) (which is also equal to 4P(4),5P(5)...) From solving simultaneous equations I got that 31a+15b+7c+3d+e=0 and similarly 211a+65b+19c+5d+e=0, but they seem rather useless at this point.

Step-by-step explanation: