How do you find the polynomial function whose graph passes through (2,4), (3,6), (5,10)?
1 Answer
May 19, 2018
Simplest solution:
#f(x) = 2x#
General solution:
#f(x) = P(x)(x^3-10x^2+31x-30)+2x#
Explanation:
Given:
#(2, 4)# ,#(3, 6)# ,#(5, 10)#
Note that each
So a suitable polynomial function is:
#f(x) = 2x#
Note however that this is not the only polynomial function passing through these three points.
We can add any multiple (scalar or polynomial) of a cubic whose zeros lie at those three points, namely:
#(x-2)(x-3)(x-5) = x^3-10x^2+31x-30#
Hence the most general solution is:
#f(x) = P(x)(x^3-10x^2+31x-30)+2x#
for any polynomial