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3 years ago

A third degree polynomial equation with rational coefficients that has roots -4 and 2+i

1 answer:

8 0

If one of the roots is 2+i, another must be 2-i. We can express this polynomial as (x+4)(x-2-i)(x-2+i). This expands to $x^3-11x+20$ .

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Solve the system of equations. 10x+y=−20 y=2x2−4x−16 ( , ) and ( , )

Sladkaya [172]

I will go about solving this using the elimination method.

First, convert the equations.

10x + y = -20
4x + y = -12

Second, find the easiest variable to get rid of and get rid of it! (In this case, y) We will subtract to get rid of y.

6x = -8

Third, you want to solve the equation.

6x = -8 (divide by 6)
x = $-1 \frac{1}{3}$

Fourth, solve for y by inserting the answer for x into one of the equations.

10( $-1 \frac{1}{3}$ ) + y = -20
$-13 \frac{1}{3}$ + y = -20 (subtract $-13 \frac{1}{3}$ )
y = $-6 \frac{2}{3}$

The solution for this system of equations is ( $-1 \frac{1}{3}$ , $-6 \frac{2}{3}$ ).

7 0

3 years ago

Read 2 more answers

How many solutions doe

musickatia [10]

Answer:

Given equation have two solutions.

x = $-\frac{5}{2} and -\frac{8}{3}$

Right option is (D)

Step-by-step explanation:

We have given,

$6x^{2} +40=-31x$

we can rewrite this equation in the form given as:

6x² + 40 + 31x = 0

or 6x² + 31x + 40 = 0

On solving this quadratic equation, we get :

x = $-\frac{5}{2} and -\frac{8}{3}$

That means, given equation have two solutions.

Right option is (D)

8 0

3 years ago

Read 2 more answers

What is the speed (approximately) of a 2.5-kilogram mass after it has fallen freely from rest through a distance of 12 meters?

Norma-Jean [14]

Answer:

15.3 m/s

Step-by-step explanation:1) Find the gravitational potential energy using the equation :

$PE_g=mgh$

$PE_g=2.5(12)(9.8)\\PE_g=294$

2) Then use the equation for kinetic energy to solve for the velocity:

$KE=\frac{1}{2} mv^{2}$

$294=\frac{1}{2}(2.5)(v^2)\\235.2=v^2\\\sqrt{235.2} =v\\15.3 m/s=v$

6 0

3 years ago

Which statements are true about ΔJKL and ΔLMN? Select all that apply.

svp [43]

Answer:

A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure $50^o,60^o,70^o$

Step-by-step explanation:

step 1

Find the value of x

we know that

$m\angle KLJ=m\angle MLN$ ----> by vertical angles

substitute the given values

$(6x-2)^o=(5x+10)^o$

solve for x

$6x-5x=10+2\\x=12$

step 2

Find the measure of the interior angles of triangle JKL

we have

$m\angle KLJ=(6(12)-2)=70^o$

$m\angle KJL=(5(12))=60^o$

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

$m\angle JKL=180^o-130^o=50^o$

therefore

Triangle JKL has angles that measure $50^o,60^o,70^o$

step 3

Find the measure of the interior angles of triangle LMN

we have

$m\angle MLN=(5(12)+10)=70^o$

$m\angle LMN=(6(12)-7)=65^o$

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

$m\angle LNM=180^o-135^o=45^o$

Triangle LMN has angles that measure $45^o,65^o,70^o$

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

Verify each statement

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure $50^o,60^o,70^o$

The statement is true (see the explanation)

Part d) ΔLMN has angles that measure $50^o,60^o,70^o$

The statement is false

Because, Triangle LMN has angles that measure $45^o,65^o,70^o$

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent

6 0

3 years ago

One of the roots of the quadratic equation 4mnx^2 – 6m^2x – 6n^2x + 9mn = 0 (m, n ≠ 0) is a)-3m/2n b)3m/2n c)2m/3n d)-2m/3n

maxonik [38]

Answer:

$B.\ \frac{3m}{2n}$

Step-by-step explanation:

Given

$4mnx^2 - 6m^2x - 6n^2x + 9mn = 0\ (m, n \neq 0)$

Required

Calculate one of the root of the equation

$4mnx^2 - 6m^2x - 6n^2x + 9mn = 0$

Factorize

$2mx(2nx - 3m) -3n(2nx - 3m) = 0$

$(2mx - 3n)(2nx - 3m) = 0$

Split equation

$2mx - 3n = 0\ or\ 2nx - 3m = 0$

Make x the subject of formula in both expressions

$2mx = 3n\ or\ 2nx = 3m$

$x = \frac{3n}{2m}\ or\ x = \frac{3m}{2n}$

From the list of given options, one of the roots of the equation is $\frac{3m}{2n}$

4 0

3 years ago