yanelicx01
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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

Respuesta :

Kimberlyalcala7
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.


davidlcastiblanco

Answer:

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

b). Function: [tex]x^{3} -10x^{2} +31x-30=0[/tex]

Step-by-step 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)

[tex]x_{1} = 2\\x_{2} = 3\\x_{3} = 5\\[/tex]

b).

[tex](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[/tex]

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