I need to find the polynomial function of degree 3.

Question

I need to find the polynomial function of degree 3. (3,-3) is the point provided and the zeros are 4 and 6.

Answer 1

All cubic polynomials have three roots.

For a cubic polynomial to have roots at x=4 and x=6, it must be of the form:

y = (x-4) (x-6) (x -r)

where r is the third root.

To pass through the point (-3, 3), we have

-3 = (3 - 4) (3 - 6) (3 - r)

Solve for r:

r = 4.

Since we are given that the other roots are at 3 and 4, then we have a double root at 4:

y = (x -6) (x - 4)²

Check: (-3,3)?

(3 - 6) (3 - 4)²

= (-3) (-1)²

= -3