Question

Write an equation for the cubic polynomial functior

Answer 1

So, the cubic polynomial function is $x^3-10x^2+31x-30=0$

No, none of the roots have multiplicity.

Step-by-step explanation:

We need to write an equation for the cubic polynomial function

whose graph has zeroes at 2, 3, and 5.

Zeros mean:

x=2, x=3 and x=5

or

x-2=0, x-3=0 and x-5=0

Multiplying all the factors:

$(x-2)(x-3)(x-5)=0\\(x-2)(x(x-5)-3(x-5))=0\\(x-2)(x^2-5x-3x+15)=0\\(x-2)(x^2-8x+15)=0\\x(x^2-8x+15)-2(x^2-8x+15)=0\\x^3-8x^2+15x-2x^2+16x-30=0\\x^3-8x^2-2x^2+15x+16x-30=0\\x^3-10x^2+31x-30=0$

So, the cubic polynomial function is $x^3-10x^2+31x-30=0$

No, none of the roots have multiplicity, A root has multiplicity if it appears more than 1 time. Like if (x-1)^2 is a root then 1 has multiplicity 2

Keywords: Polynomial Function

Learn more about Polynomial Function at:

• brainly.com/question/1414350
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• brainly.com/question/2568692

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