MATHEMATICS HIGH SCHOOL

How many roots of the polynomial 30x^4 + 7x^3-125x^2-54x+72 have absolute value greater than 1?

Answers

Answer 1

Answer:

Answer:

There are 3 roots of the given polynomial that have absolute value greater than 1.

Step-by-step explanation:

We are given the polynomial:

$p(x) = 30x^4 + 7x^3-125x^2-54x+72$

We can factorize the given polynomial as:

$p(x) = 30x^4 + 7x^3-125x^2-54x+72\n=(x-2)(2x+3)(5x-3)(3x+4)=0$

$\text{Solving for}\n(x-2) = 0\nx = 2\n|x| = 2 > 1$

$\text{Solving for}\n(2x+3) = 0\nx = (-3)/(2)\n\bigg|(-3)/(2)\bigg| = (3)/(2) > 1$

$\text{Solving for}\n(5x-3) = 0\nx = (3)/(5)\n\bigg|(3)/(5)\bigg| = (3)/(5) < 1$

$\text{Solving for}\n(3x+4) = 0\nx = (-4)/(3)\n\bigg|(-4)/(3)\bigg| = (4)/(3) > 1$

Thus, there are 3 roots of the given polynomial that have absolute value greater than 1.

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The slope of the line below is -5 which of the following is the point slope form of the line

Answers

Answer:

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (2, - 7), thus

y - (- 7) = - 5(x - 2) , that is

y + 7 = - 5(x - 2) → B

What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

Answers

The equation of circle is:
(x-a)^2+(y-b)^2=r^2 where C(a, b) is the center.
In order to find r you have to find the distance between C(-2, 1) and let's say A(-4, 1)

The formula for distance is:
$\sqrt{ ( y_(A)-y_{C )^(2) + (x_(A)- x_(C )^(2) )$
r = 2

The equation of circle is
(x+2)^2+(y-1)^2=4

I hope that this is the answer that you were looking for and it has helped you.

What is the slope of the equation 12=4x-6y

Answers

Answer:

-2/3

Step-by-step explanation:

-4x -4x

-4x+12=6y

/6 /6

-2/3+2=y

so the slope is -2/3

-2/3 that's the slope

hope this helps

find the volume of a can of chicken broth that had a diameter of 7.5cm and a height of 11cm. round 5o the neatest tenth

Answers

cans are normally cylinders
Vcylinder=hpir^2

h=11

d/2=r
7.5/2=3.75=r

V=11pi3.75^2
V=11pi14.0625
V=154.6875pi
aprox pi=3.141592 and multiply
V=485.96
round tenth
486.0 cm^3

Mr. Atinga shared his cattle among his three children Lordia,Anita,and Richmond. He gave 3/5 of cattles to Anita and shared the remaining between Lordia and Richmond in the ratio 2:3 respectively. In all 80 cattle were shared between Lordia and Richmond. How many cattle were shared among the three children How many cattle did Anita receive than Richmond

Answers

Answer:

a). The total number of cattle shared among the three children=200

b). Anita's share=120 cattle

Lordia's share=32 cattle

Richmond's share=48 cattle

Step-by-step explanation:

Step 1

Determine fraction shared between Lordia and Richmond as follows;

Lordia:Richmond=2:3

Let the total cattle be x

Lordia's fraction=2/(2+3)=2/5 of x=(2/5)x

Lordia's fraction=(2/5)x

Richmond's fraction=3/(2+3)=3/5 of x=(3/5) x

but;

x=80 cattle

replacing;

Total number of cattle Lordia got=(2/5)×80=32 cattle

Total number of cattle Richmond got=(3/5)×80=48 cattle

Step 2

Express the total cattle Mr. Atinga had initially as follows;

Let the initial number of cattle be y

The fraction remainder given to Lordia and Richmond=Initial number-fraction of the totat given to Anita

where;

Initial number=y

fraction of the total given to Anita=3/5 y

replacing;

The fraction remainder given to Lordia and Richmond=y-3/5 y=2/5 y

but;

2/5 y=80

y=80×5/2=

y=200

The total number of cattle shared among the three children=200

b).

Anita's share=(3/5)×200=120 cattle

Lordia's share=(2/5)×80=32 cattle

Richmond's share=(3/5)×80=48 cattle

Find mFraction form

Answers

Answer:

130

Step-by-step explanation:

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