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

Answer:

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)= $x^3-10x^2+31x-30$

Step-by-step 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

$(x-2)\times (x-3)\times (x-5)$

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)=$x^3-10x^2+31x-30$.