Mathematics: Write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i

Write a polynomial function of least degree with

Ответ:

Kayccee9958

10.03.2022

Mathematics

f(x)=3x^3+x^2+3x+1

Step-by-step explanation:

If a real number $-\frac{1}{3}$ is a zero of polynomial function, then

$x-\left(-\dfrac{1}{3}\right)=x+\dfrac{1}{3}$

is the factor of this function.

If a complex number is a xero of the polynomial function, then the complex number is also a zero of this function and

$x-(-i)=x+i\ \text{ and }\ x-i$

are two factors of this function.

So, the function of least degree is

$f(x)=\left(x+\dfrac{1}{3}\right)(x+i)(x-i)=\left(x+\dfrac{1}{3}\right)(x^2-i^2)=\\ \\ =\left(x+\dfrac{1}{3}\right)(x^2+1)=\dfrac{1}{3}(3x+1)(x^2+1)=\dfrac{1}{3}(3x^3+x^2+3x+1)$

If the polynomial function must be with integer coefficients, then it has a form

f(x)=3x^3+x^2+3x+1

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Ответ:

arrissa1234hinkle

07.02.2020

Mathematics

s = t - m

Step-by-step explanation:

Assuming s equals the amount of time it would take Sam, subtracting the amount of time it takes Mark from the time it takes them together would give you the time Sam would take since with Sam's help, the time would equal t hours. Then without Mark's help is how long it would take him.

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Write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i

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