Construct a polynomial function of least degree possible using the given information. Real roots: −1, 1, 3 and (2, f(2)) = (2, 5)

Question

Construct a polynomial function of least degree possible using the given information. Real roots: −1, 1, 3 and (2, f(2)) = (2, 5)

Answer 1

We can set up a polynomial in factored form with a coefficient C:

f(x)=C(x+1)(x-1)(x-3)

Plug x=2 into the polynomial, f(2)=C(2+1)(2-1)(2-3)=C(3)(1)(-1)=-3C

Since f(2)=5, 5=-3C

So, C=-5/3

Then f(x)=-5/3(x+1)(x-1)(x-3)=-5/3(x³-3x²-x+3)=-5/3x³+5x²+5/3x-5 is a polynomial of least degree that satisfies the conditions.