WILL GIVE BRAINLIEST: if the roots of the equation x^3 +px^2+qx+r = 0 are 2, 3, and 4, find the values of p, q, and r.

An equation is shown below: 1 over 2 multiplied by x plus 3 over 2 equals 2 to the power of x What is the solution to the equati

Alborosie

Answer:

First option is correct. The solution of the equation is x=1.

Step-by-step explanation:

The given equation is

$\frac{1}{2}x+\frac{3}{2}=2^x$

The value of x, which satisfy the above equation is the solution of the given equation.

Put x=1 in the given equation.

$\frac{1}{2}(1)+\frac{3}{2}=2^{1}$

$\frac{1+3}{2}=2$

$\frac{4}{2}=2$

$2=2$

Since left hand side is equal to right side, therefore first option is correct.

Put x=2 in the given equation.

$\frac{1}{2}(2)+\frac{3}{2}=2^{2}$

$\frac{2+3}{2}=4$

$\frac{5}{2}=4$

Since left hand side is not equal to right side, therefore second option is correct.

Put x=4 in the given equation.

$\frac{1}{2}(4)+\frac{3}{2}=2^{4}$

$\frac{4+3}{2}=16$

$\frac{7}{2}=16$

Since left hand side is not equal to right side, therefore third option is correct.

Put x=8 in the given equation.

$\frac{1}{2}(8)+\frac{3}{2}=2^{8}$

$\frac{8+3}{2}=256$

$\frac{11}{2}=256$

Since left hand side is not equal to right side, therefore fourth option is correct.

3 0

4 years ago

Read 2 more answers

Length=9in width=2in height=3in. what is the surface area

baherus [9]

Answer:

102in2

Step-by-step explanation:

The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.

4 0

2 years ago

Answer the following questions about the following polynomial

azamat

Answer:

There is no polynomial

Step-by-step explanation:

Show polynomial

8 0

3 years ago

I need help in problem 8 plz help me I need a a

iogann1982 [59]

Here are three ways where There could be equal rows

3*12=36
4*9=36
6*6=36

6 0

3 years ago

Carter drawers one side of equilateral triangle pqr on the coordinate plane at points P(-3, 2) and Q(5, 2). Which ordered pair i

Neko [114]

Given: Two coordinates of an equilateral triangle P(-3, 2) and Q(5, 2).

To find: Coordinate of third vertex R.

Solution: Let us take coordinate of R is (x,y).

Because we are given PQR is an equilateral triangle, all side of the triangle PQR are equal.

We can say PQ = QR = RS.

Let us find equations by using distance formula.

Distance between two coordinates is given by formula

$Distance = \sqrt{(x2-x1)^2+(y2-y1)^2}$

$PQ=\sqrt{(5-(-3))^2+(2-2)^2} = \sqrt{(5+3)^2+(0)^2} = \sqrt{8^2+0} = \sqrt{64} =8$

$QR=\sqrt{(x-5)^2+(y-2)^2} = \sqrt{x^2-10x+25 + y^2-4y+4} = \sqrt{x^2+y^2-10x-4y+29}$

$RS=\sqrt{(x-(-3)^2+(y-2)^2} = \sqrt{x^2+6x+9 + y^2-4y+4} = \sqrt{x^2+y^2+6x-4y+13}$ .

We know, PQ= QR and PQ= RS.

\sqrt{x^2+y^2-10x-4y+29}[/tex] = 8

Squaring both sides, we get

$x^2+y^2-10x-4y+29 =64$ -------- equation (1)

and \sqrt{x^2+y^2+6x-4y+13}[/tex] = 8

Squaring both sides, we get

$x^2+y^2+6x-4y+13=64$ ---------- equation (2).

Subtracting equation 2 from equation 1.

[/tex]x^2+y^2-10x-4y+29[/tex] = 64

[/tex]x^2+y^2+6x-4y+13[/tex] = 64

----------------------------------------------------

-16x +16 = 0

Subtracting 16 on both sides ,

-16x +16-16 = 0-16

-16x = -16

Dividing -16 on both sides.

-16x/-16 = -16/-16

x=1.

Plugging x=1 in first equation

$(1)^2+y^2-10(1)-4y+29 = 64$

$1+y^2-10-4y+29 = 64$ (Simplifying)

$y^2-4y+20 = 64$

Subtracting 64 from both sides.

$y^2-4y+20-64 = 64-64$

$y^2-4y-44 = 0$

By using quadratic formula..

$y=\frac{-(-4)+\sqrt{(-4)^2-4(1)(-44)} }{2(1)} and$

$y=\frac{-(-4)-\sqrt{(-4)^2-4(1)(-44)} }{2(1)} [tex]y=2\left(1+2\sqrt{3}\right),\:y=2\left(1-2\sqrt{3}\right)$

In decimal form

y=8.928, -4.928.

Therefore, coordinates of vertex R could be (1, 8.928) or (1, -4.928).

7 0

3 years ago