construct a polynomial function of least degree possible using the given information.

Question

How to solve this question?

construct a polynomial function of least degree possible using the given information

Question:

Real roots: -2, 1/2 (with multiplicity 2) and

(-3,f(-3))=(-3,5)

Answer 1

Hi,

Real roots: -2, 1/2 (with multiplicity 2) and

(-3,f(-3))=(-3,5)

x = -2 ---> (x+2) is one of factors of polynomial

unfortunately this question is not very clear that (with multiplicity 2) works for -2 & 1/2 or only for 1/2 I made a decision only for 1/2

x = 1/2 ---> ( x - 1/2)^2 is another factor of polynomial

(-3,f(-3))=(-3,5) means f(-3) = 5 and works for finding coefficient of polynomial

AT LEAST the polynomial will be:

p(x) = k ( x+2)(x-1/2)^2 with replacing -3 at this expression we will have:

p(-3) = k ( -3+2)(-3-1/2)^2 = 5

k(-1)(-3.5)^2 = 5

k = -5/12.25 = -20/49

so p(x) = -20/49 ( x+2)(x-1/2)^2

if multiplicity works for -2 also we will have p(x) = 20/49 ( x+2)^2(x-1/2)^2

I hope it is useful, please let me know if you have any question.

Minoo