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irga5000 [103]
4 years ago
12

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the ste

ps for writing the equation of this cubic polynomial function.
Mathematics
2 answers:
nika2105 [10]4 years ago
6 0
Let x=a be the same zeros for the polynomial.
The function is of the form
y = b(x - a)^3
where b  is a constant.

Because the curve passes through (0, -5), therefore
-5 = b(-a)^3  => b = 5/a^3

The equation for the polynomial is
y = (5/a^3)*(x-a)^3
   = 5(x/a - 1)^3

Answer: y = 5(x/a - 1)^3

Dmitrij [34]4 years ago
3 0

Answer:

The cubic polynomial is y=5(\frac{x}{a}-1)^3.

Step-by-step explanation:

It is given that the degree of the polynomial is 3 and the polynomial has same roots. The polynomial passing through (0,-5).

The polynomial function is defined as

P(x)=c(x-a_1)^{m_1}(x-x_2)^{m_2}...(x-x_n)^{m_n}

Where c is a constant, a_1,a_2,....,a_n are roots with multiplicity m_1,m_2,...,m_n.

Since the degree of the polynomial is 3 and it has same roots therefore the multiplicity of root is 3.

y=c(x-a)^3

The polynomial passing through (0,-5).

-5=c(0-a)^3

-5=c(-a)^3

5=ca^3

c=\frac{5}{a^3}

So the equation of the polynomial is,

y=\frac{5}{a^3}(x-a)^3

y=5(\frac{x-a}{a})^3

y=5(\frac{x}{a}-1)^3

Where a is the root of polynomial.

Therefore the cubic polynomial is y=5(\frac{x}{a}-1)^3.

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