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alina1380 [7]
3 years ago
9

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

Mathematics
2 answers:
TiliK225 [7]3 years ago
7 0

we know that

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function. The term multiplicity, refers to the number of times that its associated factor appears in the polynomial.

So

In this problem

If the cubic polynomial function has zeroes at 2, 3, and 5

then

the factors are

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

Part a) Can any of the roots have multiplicity?

The answer is No

If a cubic polynomial function has three different zeroes

then

the multiplicity of each factor is one

For instance, the cubic polynomial function has the zeroes

x=2\\ x=3\\ x=5

each occurring once.

Part b) How can you find a function that has these roots?

To find the cubic polynomial function multiply the factors and equate to zero

so

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

therefore

the answer Part b) is

the cubic polynomial function is equal to

x^{3}-10x^{2} +31x-30=0

Artemon [7]3 years ago
5 0
The quadratic function x^2 - 5x  + 6 =0
can 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.

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Montraie has a coin collection. He keeps 10 of the coins in his box, which is 20% of the collection. How many total coins are in
jek_recluse [69]

By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.

<h3>How to calculate the quantity of coins in a collection</h3>

In this question we know the quantity of coins in a box and such coins are part of the <em>coin</em> collection. By definition of percentage we have the <em>total</em> quantity of coins in the collection:

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By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.

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What set of reflections would carry hexagon ABCDEF onto itself?
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When a set of reflections that carry a shape onto itself, it means that the final position of the shape will be the same as its original location

Reflections <em>(a) y=x, x-axis, y=x, y-axis </em>would carry the hexagon onto itself

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(x,y) \to (y,x)

The rule of reflection across the x-axis is:

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So, we have:

(y,x) \to (y,-x)

The rule of reflection y =x is:

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So, we have:

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So, the overall transformation is:

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Notice that, the original and final coordinates are the same.

This means that:

Reflections <em>(a) y=x, x-axis, y=x, y-axis </em>would carry the hexagon onto itself

Read more about reflections at:

brainly.com/question/938117

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