Let f(x) be a monic 4th degree polynomial such that f(1) = 1, f(2) = 8, f(3) = 27, f(4) = 64. Find f(5).
f(x)=x^4 + ax^3 + bx^2 + cx +d
1 + a + b + c + d = 1
16+8a+4b+2c+d = 8
81+27a+9b+3c+d=27
256+64a+16b+4c+d=64
Solving via Wolfram Alpha:
a = -9 and b = 35 and c = -50 and d = 24
In Matlab:
>> a = -9 , b = 35 , c = -50 , d = 24
a =
-9
b =
35
c =
-50
d =
24
>> for x=sym(1):5 x^4+a*x^3+b*x^2+c*x+d
end
ans =
1
ans =
8
ans =
27
ans =
64
ans =
149
f(5) = 149
Edited on January 12, 2025, 8:52 am
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Posted by Charlie
on 2025-01-12 08:51:11 |
computer solution
