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Marina CMI [18]
3 years ago
9

Solve for N. -N/5 = -5

Mathematics
1 answer:
VikaD [51]3 years ago
6 0

Answer:

5

Step-by-step explanation:

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Read 2 more answers
Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. Write the function in sta
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Answer:

f(x)=x^3+(3+\sqrt{5})x^2+(6\sqrt{5}-18)x

or

f(x)=x^3+3x^2+\sqrt{5}x^2-18x+6\sqrt{5}x

Step-by-step explanation:

A polynomial function with 3 zeroes is going to be of degree 3, so we're going to have at least least 3 factors of the form x-a, where <em>a </em>is a zero of the function. For three zeroes <em>a</em>, <em>b</em>, and <em>c</em>, we'd have the factors x-a,\ x-b, and x-c, making our function look like

f(x)=(x-a)(x-b)(x-c)

Substituting our roots for a, b, and c:

f(x)=(x-(-6))(x-0)(x-(3-\sqrt{5}))\\=(x+6)(x)(x-3+\sqrt{5})

To write this function in standard form, we can expand from left to right:

f(x)=(x^2+6x)(x-3+\sqrt{5})\\=(x^2+6x)x-(x^2+6x)3+(x^2+6x)\sqrt{5}\\=x^3+6x^2-3x^2-18x+\sqrt{5}x^2+6\sqrt{5}x\\=x^3+3x^2+\sqrt{5}x^2-18x+6\sqrt{5}x

At this point, we could either leave it as is, or group the coefficients for the x^2 and x terms to get

f(x)=x^3+(3+\sqrt{5})x^2+(6\sqrt{5}-18)x

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4 years ago
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