Question

Help!!!!!!

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Can any of the roots have multiplicity? How can you find a function that has these roots?

Answer 1

I set up these three factors
(x-2) * (x-3) * (x-5) and then multiplied these to get this equation:

x^3 -10x^2 +31x -30 = 0

Answer 2

The cubic polynomial function whose graph has zeroes at2,3,5 is given by

`x^3-10x^2+31x-30`.

No, any of the roots ave no multiplicity.

The function P(x)=
`x^3-10x^2+31x-30`

Explanation:

Given graph has zeroes at 2, 3and 5

x=2

x-2=0

x=3

x-3=0

x=5

x-5=0

Multiply (x-2) , (x-3) and (x-5)

We get

`(x-2)* (x-3)* (x-5)`

after multiply we get an equation of cubic polynomial

=
`x^3-10x^2+31x-30`

Multiplicity : If a value of root repeated then the repeated value of root is called multiplicity.

Therefore , any root have no multiplicity because value of any root not repeated.

The function that has these roots is given by

p(x)=
`x^3-10x^2+31x-30`.