what are the roots of the polynomial equation

Answer:

One possible equation is [tex]f(x) = (x + 3)\, (x - 5)[/tex], which is equivalent to [tex]f(x) = x^{2} - 2\, x - 15[/tex].

Step-by-step explanation:

The factor theorem states that if [tex]x = x_{0}[/tex]  (where [tex]x_{0}[/tex] is a constant) is a root of a function, [tex](x - x_{0})[/tex] would be a factor of that function.

The question states that [tex](-3,\, 0)[/tex] and [tex](5,\, 0)[/tex] are [tex]x[/tex]-intercepts of this function. In other words, [tex]x = -3[/tex] and [tex]x = 5[/tex] would both set the value of this quadratic function to [tex]0[/tex]. Thus, [tex]x = -3\![/tex] and [tex]x = 5\![/tex] would be two roots of this function.

By the factor theorem, [tex](x - (-3))[/tex] and [tex](x - 5)[/tex] would be two factors of this function.

Because the function in this question is quadratic, [tex](x - (-3))[/tex] and [tex](x - 5)[/tex] would be the only two factors of this function. In other words, for some constant [tex]a[/tex] ([tex]a \ne 0[/tex]):

[tex]f(x) = a\, (x - (-3))\, (x - 5)[/tex].

Simplify to obtain:

[tex]f(x) = a\, (x + 3)\, (x - 5)[/tex].

Expand this expression to obtain:

[tex]f(x) = a\, (x^{2} - 2\, x - 15)[/tex].

(Quadratic functions are polynomials of degree two. If this function has any factor other than [tex](x - (-3))[/tex] and [tex](x - 5)[/tex], expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of [tex]a[/tex] corresponds to a distinct quadratic function with [tex]x[/tex]-intercepts [tex](-3,\, 0)[/tex] and [tex](5,\, 0)[/tex]. For example, with [tex]a = 1[/tex]:

[tex]f(x) = (x + 3)\, (x - 5)[/tex], or equivalently,

[tex]f(x) = x^{2} - 2\, x - 15[/tex].

Answer:

y=6x-4

(dark blue)

Step-by-step explanation:

x=0 y=-4

y=6x-4

y=6(0)-4

y=-4

Answer:

I hope this works

Step-by-step explanation:

look at the picture

Answer:

8:9

Step-by-step explanation:

enter

9

-----

8

The value of q when q varies inversely with p is 2.

The formula that can be used to represent inverse variation is:

p = k/q

Where:

The first step is to determine the value of the constant of proportionality

k = p x q

k = 15 x 4 = 60

Given the value of the  constant of proportionality, the value of q can now be determined.

30 = 60/q

q = 60 / 30

q = 2

To learn more about inverse proportion, please check: https://brainly.com/question/25748643

Answer:

d

Step-by-step explanation:

-4 < 2x +4

-8 < 2x

-8/2

-4 < x

other side

2x + 4 < 8

8-4

2x < 4

4/2

x < 2

Answer:

The answer (as i checked i recommended doing is D)

Answer:

The answer is 110.

Step-by-step explanation:

Area = 1/2 ( 9 + 13) 10

1/2 ( 22 ) 10 = 110

Answer:

x = 5 , y = 2

Step-by-step explanation:

3y + 4y + 2x = 24

(3y)² + (4y)² = (2x)²

2x + 7y = 24 .............. (1)

25y² = 4x² ................ (2)

x = [tex]\frac{5}{2}[/tex] y   ------>  (1)  

2 ( [tex]\frac{5}{2}[/tex] y ) + 7y = 24

12y = 24

y = 2 ----------> (1)

x = 5

0.7 as a fraction:

Answer:

The two marked in the image.

Step-by-step explanation:

In scientific notation you will want only the most significant non-zero digit before the comma.

The first underlined number has two digits before it, the correct representation should be [tex]1.25\times10^4[/tex]

The second underlined number has a 0 leading digit, while the most significant non-zero digit is a 4. The correct represantation should be [tex]4.5\times 10^2[/tex]

An extra case could be made for the second number of the list, since it has no decimal part, but the way I read it means "the instrument used to measure the data has 0 decimal places accuracy"

[tex]\orange{\bigstar\underline{\underline {\pmb{\frak{ \purple{Required~Answer}}}}}}[/tex]

Given:.

Steps :

470 × 0.88

£413.6

Answer:

X= 48°

Step-by-step explanation:

please mark me brainiest

++++++++++++++

Answer:

A die has 6 numbers.

So 6 numbers them being
1, 2, 3, 4, 5, 6

There’s only one number greater then 5 which is 6.
Since its 6 numbers, a die has a 1/6 chance of getting your desired number.

So it’s a 1/6 chance.

Answer:

15/8

Step-by-step explanation:

I believe you mean 5 and 3/8, if that so well here's your answer:

Domenator (bottem number) stays same, numerator (top number) is timesed by the whole number (non-fraction number/left number)

So that'll be 5 * 3 = 15 making 15/8

Answer

₹1344

Step-by-step explanation:

Principle(P) =₹1,200

Rate of Interest(R)=4pc.pa

Time(T)=3years

Simple interest=?

S.I.=P×R×T/100

=1,200×4×3/100

S.I.=₹144

amount=interest+principle

=144+1200

=1344rupees

Answer:

$1349.84

Step-by-step explanation:

→ Find the multiplier

( 100 + 4 ) ÷ 100 = 1.04

→ Multiply this by amount raised to the power of 3

1200 × 1.04³ = 1349.84

Answer:

it's 9

Step-by-step explanation:

you add up the numbers

Answer:

the answer is 9, if adding

Answer:

13 teams and 3 people left over

Step-by-step explanation:

55/4 would be 13 with a remainder of 3. That 3 would be the number of people left over. And 13 would be the number of groups of four available.

Answer:

Rs 1210

Step-by-step explanation:

cost price = (100/100+10/100)×selling price

Answer:

D. 2.5

I hope it's help.......

Using proportions, it is found that:

A proportion is a fraction of a total amount.

In the sample, the most voted options were checking out books or studying, hence:

The most popular choice likely be either checking out books or studying.

Out of the 60 students, 10 = 1/6 are doing research, hence out of 540:

[tex]\frac{1}{6} \times 540 = 90[/tex]

Based on the sample, about 90 students will vote for doing research.

21 out of 60 students voted for checking out books, hence:

21/60 = 0.35 = 35%.

Based on the sample, about 35% of students will for checking out books.

More can be learned about proportions at https://brainly.com/question/24372153

Answer: Look at the attachment

Checking out books or studying

90

35%

Step-by-step explanation:

Answer:

[tex]S = 276\ in^2[/tex]

Step-by-step explanation:

Step 1:  Determine important information

Using the given numbers it doesn't really matter which is which because the equation multiplies everything together.

Surface Area of a Rectangular Prism → [tex]S= 2(wl+hl+hw)[/tex]

Step 2:  Plug in the values and solve

[tex]S = 2((10\ in * 4\ in) + (7\ in * 4\ in) + (7\ in * 10\ in))[/tex]

[tex]S=2(40\ in^2 + 28\ in^2 + 70\ in^2)[/tex]

[tex]S = 2(138\ in^2)[/tex]

[tex]S = 276\ in^2[/tex]

Answer: [tex]S = 276\ in^2[/tex]

Answer:

Step-by-step explanation:

We already know that both triangles have a congruent side length.

We also know angle KVM or UVW are the same

We only have to know if VM and WV are the same.

This way, each triangle will have two congruent side lengths and a angle. The third side will therefore be the same.

By the same logic, if we know that KM and UW are the same, the two triangles are also congruent.

To determine if two triangles are congruent using the SAS (Side-Angle-Side) criterion, we need additional information about the length of one side, the measure of one angle, and the length of another side in both triangles.

This information is crucial in order to establish the congruence between the triangles. For example, let's consider two triangles, triangle ABC and triangle DEF. To prove that these triangles are congruent using the SAS criterion, we need to know: 1. The length of side AB in triangle ABC and the length of side DE in triangle DEF. 2. The measure of angle A in triangle ABC and the measure of angle D in triangle DEF. 3. The length of side BC in triangle ABC and the length of side EF in triangle DEF. By knowing these measurements, we can compare the corresponding sides and angles of the two triangles. If the lengths of the corresponding sides are equal and the measures of the corresponding angles are equal, then we can conclude that the two triangles are congruent by the SAS criterion.

To know more about hypotenuse here

https://brainly.com/question/2217700

#SPJ2

Answer:

A. x² - 2x - 8

Step-by-step explanation:

At x = -2, 4 graph cut x- axis. So, they are zeroes of f(x).

So, f(x) = k(x+2)(x-4), where k is a constant.

Now, (3, -5) in f(x), we get

-5 = k (3+2)( 3 -4)

-5 = -5k

k= 1

So, f(x) =  (x+2)(x-4)

= x² - 2x - 8

So, option A is right.

Answer:

so add the ones that are given and then subtract from 360 because they must total to 360. so 360-80-68-84-56-40=32 so A

Answer:

Step 3.

Step-by-step explanation:

If you look at the equation you can see that that -9 is gone from the left from being added by 9 and -4 is the result of 9 being added to -13. Step 2 would not be the correct answer because they haven't added the numbers yet. Hope this helps!

Answer: step 3

Step-by-step explanation:

answer: C

you can use "bedmas". In the an equation you're doing, one of the first steps would to be to deal with exponents since there's no brackets and C is the only one with the exponents done.

Answer: 2

Step-by-step explanation:

Answer:

140

Step-by-step explanation: