All categories

2 years ago

Write a polynomial function of the least degree with integral coefficients that has the given zeros.

Mathematics

1 answer:

Mkey [24]2 years ago

6 0

Step-by-step explanation:

Degree: 3

Zeros: -3, 3 + √3i

Solution point: f(-1) = -172

(a) Write the function in completely factored form.

f(x) =

(b) Write the function in polynomial form.

f(x) =

You might be interested in

Alex sold wrapping paper rolls (r) as part of a school fundraiser. He earned a total of 165 reward points from his sales. Using

Dafna11 [192]

He sold 66 wrapping paper because all you want to do is divide

5 0

3 years ago

An isosceles triangle ABC has legs of length 24 and a vertex angle that measures 36º . Determine the length of its base, BC , to

iris [78.8K]

Answer: $BC=14.8$

Step-by-step explanation:

By definition, an Isosceles triangle has two equal sides and its opposite angles are congruent.

Observe the figure attached, where the isosceles triangle is divided into two equal right triangles.

So, in this case you need to use the following Trigonometric Identity:

$sin\alpha =\frac{opposite}{hypotenuse}$

In this case, you can identify that:

$\alpha =\angle BAD=\angle CAD=18\°\\\\opposite=BD=CD=x\\\\hypotenuse=AB=AC=24$

Substituting values, and solving for "x", you get:

$sin(18\°)=\frac{x}{24}\\\\24*sin(18\°)=x\\\\x=7.416$

Therefore, the length of BC rounded to nearest tenth, is:

$BC=2(7.416)=14.8$

6 0

2 years ago

Find the limit

Lana71 [14]

Step-by-step explanation:

<h3>Appropriate Question :-</h3>

Find the limit

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

On substituting directly x = 1, we get,

$\rm \: = \: \sf \dfrac{1-2}{1 - 1}-\dfrac{1}{1 - 3 + 2}$

$\rm \: = \sf \: \: - \infty \: - \: \infty$

which is indeterminant form.

Consider again,

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

can be rewritten as

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]$

$\rm \: = \: \sf \: \dfrac{1 - 3}{1 \times (1 - 2)}$

$\rm \: = \: \sf \: \dfrac{ - 2}{ - 1}$

$\rm \: = \: \sf \boxed{2}$

Hence,

$\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}$

$\rule{190pt}{2pt}$

7 0

2 years ago

Read 2 more answers

Whats the area of a polygon with vertices A(2,3) B(12,3) C(6,0) and D(2,0)

Vanyuwa [196]

This shape is trapezoid

top of the trapezoid is 10 (12-2)

and the bottom is 4 (6-2)

the height in 3 (3-0)

so the area will be
$((10+4) \times 3) \div 2 \\ = (14 \times 3) \div 2 = 42 \div 2 \\ = 21$
the area is 21

6 0

3 years ago

Glenn bought 3 pounds of tomatoes. He used 5/8 of them to make sauce.

n200080 [17]

<em>Question Continuation:</em>

<em>Glenn bought 3 pounds of tomatoes. He used 5/8 of them to make sauce. </em>

<em>Make an equation that shows the number of pounds of tomatoes Glenn used for the sauce.</em>

Answer:

$y = \frac{15}{8}\ lb$

Step-by-step explanation:

Given

Weight of Tomato = 3 lb

Used Proportion = 5/8

Required

Determine the portion used

To solve this we simply multiply the used proportion by the weight of the tomato bought

Represent the used portion with y.

So:

$y = Weight * Used\ Proportion$

$y = 3\ lb * \frac{5}{8}$

$y = \frac{15}{8}\ lb$

4 0

3 years ago