The polynomial of degree 4, P(x) has a root of

Iris Vaughan

Iris Vaughan

Answered question

2022-02-01

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,112). How do you find a formula for P(x)?

Answer & Explanation

venenolundicoofw

venenolundicoofw

Beginner2022-02-02Added 12 answers

A polynomial of degree 4 will have the root form:
y=k(xr1)(xr2)(xr3)(xr4)
Substitute in the values for the roots and then use the point to find the value of k.
Explanation:
Substitute in the values for the roots:
y=k(x-0)(x-3)(x-3)(x-(-3))
Use the point (5,112) to find the value of k:
112=k(5-0)(5-3)(5-(-3))
112=k(5)(2)(2)(8)
k=112(5)(2)(2)(8)
k=710
The root from of the polynomial is:
y=710(x0)(x3)(x3)(x(3))

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?