C^2 + 5c =3 Tell if this factors or not? And show how it factors or does not factor? And if it factors what are the roots?

Answers

Answer 1

Answer: The answer to your questions is that it depends on how we view the polynomial. In particular,

$c^2+5c=3\implies c^2+5c-3=0$

If the left hand side were factorizable, then we would be able to write it in the form

$(c-r_1)(c-r_2)=c^2+5c-3=0$

If we expand the leftmost expression, we'd get

$c^2-(r_1+r_2)c+r_1r_2=c^2+5c-3=0$

and so for the two polynomials to be the same, the coefficients must match. In other words, the unknowns $r_1,r_2$ would have to satisfy

$\begin{cases}-(r_1+r_2)=5\nr_1r_2=-3\end{cases}$

Suppose that, moreover, we want integer solutions for $r_1,r_2$ . For this to happen, they must be factor pairs of the constant term.

-3 only has two factor pairs. Either $r_1=-1$ and $r_2=3$ , or $r_1=1$ and $r_2=-3$ . In the first case, we'd get a linear coefficient of $-(-1+3)=-2\neq5$ , while in the second, we'd get $-(1-3)=2\neq5$ .

There is no integer solution for this system, so the original quadratic is not factorizable - but only so over the integers.

If we change the scope of the coefficients, i.e. allow for any real numbers/complex numbers to appear in the factorization, then we always factorize a quadratic. The above system is easy to solve.

$r_1r_2=-3\implies r_2=-\frac3{r_1}$
$\implies-\left(r_1-\frac3{r_1}\right)=5$
$\implies{r_1}^2+5r_1-3=0$
$\implies r_1=\frac{-5\pm√(37)}2$

$\implies c^2+5c-3=\left(c+\frac{5-√(37)}2\right)\left(c+\frac{5+√(37)}2\right)$

so the original quadratic is factorizable over the reals.

Related Questions

HELP IT'S DUE TONIGHT!!!!! If a piece of steel 12 feet long weighs 168 pounds, how much will a piece of steel 20 feet long weigh?
Could someone please help?Find the perimeter of each figure.
The cost of having a package delivered has a base fee of $10.80. Every pound over 5 lbs cost an additional $0.41 per pound. Write an equation that expresses the cost C in terms of w, the total weight in pounds of a package weighing over 5 lbs. a. C = 10.8w + 0.41 c. C = 0.41(w - 5) + 10.8 b. C = 0.41w + 10.8 d. C = 0.41w + 12.85
A sphere fits snugly inside a cube with 2.4 m. edges. What is the approximate volume of the space between the sphere and cube to the nearest tenth?
Help as quick and i will give the brainliest!!!

Find the value of k so that the graph of the equation has the given y-intercept. y = − 1 /3x + 5/6 k; b = −10

Answers

i think k is 5 but if i am wrong srry hope it helped

A central angle θ in a circle of radius 3 m is subtended by an arc of length 4 m. Find the measure of θ in degrees. (Round your answer to one decimal place.) θ = ° Find the measure of θ in radians. (Round your answer to two decimal places.) θ = rad

Answers

Answer:

θ = 76.4°

θ = 1.33 radians

Step-by-step explanation:

Length of an arc is given as

L = (θ/360) × 2πr

L = 4 m

θ = angle subtended at the centre of the circle by the arc in degrees = ?

r = radius of the circle = 3 m

4 = (θ/360) × 2π(3)

θ = (4×360)/6π

θ = 76.4°

L = θ r

where θ = angle subtended at the centre of the circle by the arc in radians

4 = θ × 3

θ = (4/3) = 1.33 radians

OR we could do a direct conversion

360° = 2π radians

76.4° = (76.4 × 2π)/360

θ = (4/3) radians = 1.33 radians

Hope this Helps!!!

Step-by-step explanation:

Below is an attachment containing the solution.

Solve for the portion. Round to hundredths when necessary.What is the portion if the base is 1,850 and the rate is 150%?

Answers

The portion is $2,475 if the base is 1,850 and the rate is 150%.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

We have to determine the portion if the base is 1,850.

Here rate is 150% or 150/100 = 1.50.

The base = 1,650.

Since the portion is the multiplication of base and rate.

The portion = base × rate.

The portion = 1650 × 1.50.

The portion = $2,475

Therefore, the portion is $2,475 if the base is 1,850 and the rate is 150%.

Answer:

portion = base * rate. rate is 150% or 150/100 = 1.50. base = 1,650. portion = 1650*1.50. portion = $2,475

Step-by-step explanation:

plz mark brainliest!!!!!!!!!!!!!!!!!!!!!!!!

Convert the fractions to decimal numbers.

Answers

Answer: 0.5 as decimal 50% as pertange hope i helped

Step-by-step explanation: <3

Answer:

0.5

Step-by-step explanation:

Hopethatthisishelpful.

Haveagreatday.

Which of the following could be the areas of the three squares.
40 , 55, 95