Question

Write an equation for the cubic polynomial function whose graph has zeros at 2,3 & 5.

can any of the roots have multiplicity ?
how can you find a function that has these roots ?


i need the answer asap please

Answer 1

The quadratic function x^2 - 5x + 6 =0can be factored into (x -3) * (x-2)And it would have roots of 3 and 2
So, if a cubic functions has roots of 2, 3 and 5 then its factors are (x -2)* (x -3) * (x -5)Multiply it out to get the equation.

Answer 2

a). No multiplicity the roots have factor one each one

b). Function:
`x^(3) -10x^(2) +31x-30=0`

Explanation:

a).

No a cubic polynomial function only have 3 roots and they are already find so the factor is one

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

`x_(1) = 2\\x_(2) = 3\\x_(3) = 5\\`

b).

`(x-2)*(x-3)*(x-5)=0\\(x^(2) -2x-3x+6)*(x-5)=0\\(x^(2) -5x+6)*(x-5)=0\\x^(3) -5x^(2)+6x -5x^(2) +25x -30=0\\x^(3) -10x^(2)+31x -30=0`