So, the cubic polynomial function is [tex]x^3-10x^2+31x-30=0[/tex]
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:
[tex](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\\[/tex]
So, the cubic polynomial function is [tex]x^3-10x^2+31x-30=0[/tex]
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
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Answer: The roots can't have multiplicity because the function is specified as cubic and 3 roots are given. To find the function, write f(x) (x 2)(x 3)(x 5), and simplify the right side.
Step-by-step explanation:
This is a shorter answer for those who don't want too much words on their assignment. But still give the first answer credit as they put effort into their answer and also are correct.
