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Zielflug [23.3K]
3 years ago
13

X (number of hours) 1 2 3 4 y (earnings in dollars) 8 20 32 44

Mathematics
1 answer:
Lena [83]3 years ago
6 0
Dndnd sbshsjsjss shahs
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Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots StartRoo
spayn [35]

Answer:

f(x)=3x^3-6x^2-15x+30

Or

f(x)=3(x-2)(x+\sqrt{5})(x-\sqrt{5})

Step-by-step explanation:

For a polynomial function of lowest degree with rational real coefficients, each root has multiplicity of 1.

The polynomial has roots x=\sqrt{5} and 2 with a leading coefficient of 3.

By the irrational root theorem of polynomials, x=-\sqrt{5} is also a root of the required polynomial.

By the factor theorem, we can write the polynomial in factored form as:

f(x)=3(x-2)(x+\sqrt{5})(x-\sqrt{5})

We expand, applying difference of two squares to obtain

f(x)=3(x-2)(x^2-5)

We expand further using the distributive property to get:

f(x)=3x^3-6x^2-15x+30

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