Write a polynomial f(x) that satisfies the given conditions.

Degree 3 polynomial with integer coefficients with zeros −3i and 9/5.

Degree 3 polynomial with integer coefficients with zeros −3i and 9/5.

Lorraine Harvey
2021-12-12
Answered

Write a polynomial f(x) that satisfies the given conditions.

Degree 3 polynomial with integer coefficients with zeros −3i and 9/5.

Degree 3 polynomial with integer coefficients with zeros −3i and 9/5.

You can still ask an expert for help

vicki331g8

Answered 2021-12-13
Author has **37** answers

Step 1

Here we write a polynomial function of 3 with zeros −3i and 9/5.

Step 2

Let f(x) be the ploynomial function

Since −3i be the zeros of f(x) then +3i be also zeros of f(x)

[because complex conjugate each other]

Since −3i be the zeros of f(x) then (x+3i) be the factor of f(x).

Since +3i be the zeros of f(x) then (x−3i) be tge factor of f(x)

Since 9/5 be the zeros of f(x) , then (x−9/5) be the factor of f(x).

Step 3

Therefore f(x)=(x+3i)(x−3i)(x−9/6)

$=({x}^{2}-{\left(3i\right)}^{2})(x-\frac{9}{5})$

$={x}^{2}(x-\frac{9}{5})+9(x-\frac{9}{5})$

$={x}^{3}-\frac{9{x}^{2}}{5}+9x-\frac{81}{5}$

$={x}^{3}-\frac{9{x}^{2}}{5}+9x-\frac{81}{5}$

Hence$f\left(x\right)={x}^{3}-\frac{9{x}^{2}}{5}+9x-\frac{81}{5}$

Here we write a polynomial function of 3 with zeros −3i and 9/5.

Step 2

Let f(x) be the ploynomial function

Since −3i be the zeros of f(x) then +3i be also zeros of f(x)

[because complex conjugate each other]

Since −3i be the zeros of f(x) then (x+3i) be the factor of f(x).

Since +3i be the zeros of f(x) then (x−3i) be tge factor of f(x)

Since 9/5 be the zeros of f(x) , then (x−9/5) be the factor of f(x).

Step 3

Therefore f(x)=(x+3i)(x−3i)(x−9/6)

Hence

Nadine Salcido

Answered 2021-12-14
Author has **34** answers

Zeros -3i and $\frac{9}{5}$

Complex zero must have conjugate

$x=\pm 3i\text{}x=\frac{9}{5}$

$f\left(x\right)=(x-3i)(x+3i)(x-\frac{9}{5})$

$=({x}^{2}-{\left(3i\right)}^{2})(x-\frac{9}{5})$

$=({x}^{2}+9)(x-\frac{9}{5})$

$={x}^{3}+9x-\frac{9}{5}{x}^{2}-\frac{81}{5}$

$={x}^{3}-\frac{9}{5}{x}^{2}+9x-\frac{81}{5}$

Complex zero must have conjugate

asked 2021-06-03

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

$g(x)=3-\frac{{x}^{2}}{4}$

asked 2022-01-16

Consider the following polynomials over $Z}_{8$ where a is written for [a] in $Z}_{8$ :-

$f\left(x\right)=2{x}^{3}+7x+4,g\left(x\right)=4{x}^{2}+4x+6,h\left(x\right)=6{x}^{2}+3$ .

Find each of the following polynomials with all coefficients in$Z}_{8$ ,

f(x)g(x)+h(x)

Find each of the following polynomials with all coefficients in

f(x)g(x)+h(x)

asked 2021-04-04

To perform: The operation [43]+[32] in $Z}_{11$ and indicate the answer in [r] where $0\le r\le m$ .

asked 2021-12-28

For the following exercises, find the degree and leading coefficient for the given polynomial.

$x(4-{x}^{2})(2x+1)$

asked 2021-12-04

All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

$P\left(x\right)={x}^{3}+5{x}^{2}-x-5$

x=

Write the polynomial in factored form.

P(x) =

x=

Write the polynomial in factored form.

P(x) =

asked 2021-12-07

Factor the polynomial completely, and find all its zeros. State the multiplicity of each zero.

$P\left(x\right)=16{x}^{4}-81$

asked 2022-02-03

How do you write the equation y=-1.7x+8.5 in standard form?