All categories

2 years ago

What is the solution to the following equation? x2 + 3x + 4 = 0

Mathematics

1 answer:

andreev551 [17]2 years ago

5 0

Answer:

$x=\dfrac{-3\pm \sqrt7i}{2}$

Step-by-step explanation:

The given equation is $x^{2}+3x+4=0$ .

We need to find the solution of the above equation.

The solution of an equation $ax^2+bx+c=0$ is :

$x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

We have, a = 1, b = 3 and c = 4

$x=\dfrac{-3+ \sqrt{(3)^2-4(1)(4)} }{2}, \dfrac{-3- \sqrt{(3)^2-4(1)(4)} }{2}\\\\=\dfrac{-3+\sqrt{9-16}}{2}, \dfrac{-3-\sqrt{9-16}}{2}\\\\=\dfrac{-3\pm \sqrt7i}{2}$

So, the solution of the given equation is $\dfrac{-3\pm \sqrt7i}{2}$ .

You might be interested in

A person who weighs 100 pounds on Earth weighs 16.6 lb. on the moon.

mario62 [17]

Answer:

See explanation below.

Step-by-step explanation:

Given: 100 lbs on Earth is 16.6 lbs on the moon.

a. The independent variable is weight. The gravity of the Moon and the gravity of the Earth are constant. Weight can change, but gravity is a constant.

b. An equation that relates the weight of someone on the Moon who travels to the Earth:

100 / 16.6 = 6.02. Take the Moon weight and multiply by 6.02:

Moon Weight * 6.02 = Earth Weight.

Proof:

16.6 * 6.024 = 99.99 - approximately 100 lbs Earth weight.

c. A 185 lb astronaut on Earth would weigh:

16.6 / 100 = .166. Take the Earth weight and multiply by .166:

185 * .166 = 30 lbs on the Moon.

d. A person who weighs 50 lbs on the Moon:

50 * 6.024 = 301.2 lbs on Earth.

Hope this helps! Have an Awesome Day! :-)

6 0

3 years ago

Part 2. State what additional information is required in order to know that the triangles are congruent by ASA.

Helga [31]

<h3>Answer: Choice D. $\angle SQR \cong \angle XQR$ </h3>

The red angle markers show those two angles are congruent. That's one "A" of "ASA". The S refers to a congruent pair of sides. We don't have any tickmarks to indicate congruent pairs; however, we do know that QR = QR is a shared side that overlaps (reflexive theorem). So this is the "S" in "ASA".

The thing missing is the angle Q of the top triangle, and also of the bottom triangle as well. If we know those two angles are congruent, then we have enough info to use ASA. More specifically, if we know that $\angle SQR \cong \angle XQR$ , then we can use ASA.

One thing to notice is that the other answer choices involve side lengths and not angles. This implies that if A, B or C were one of the answers, then we would have something like SAS or SSS. But instead we want ASA. So we can immediately rule choices A,B, and C out.

7 0

2 years ago

A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

$f(g(x))= f(\frac{2x+1}{x} )$

$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

$g(\frac{1}{x-2} )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

For the Composition function $f(g(x)) = f(\frac{2x+1}{x} )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g(\frac{1}{x-2} )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

8 0

3 years ago

What is the equation of a horizontal line passing through the point (2, 10)?

Romashka [77]

Answer:

O x = 2

Step-by-step explanation:

Only x-intercepts will make the line horizontally and x = 2 is the line that passes through the point (2, 10)

7 0

3 years ago

Bella is planning to write in a journal some pages will have one journal entry on them and other pages will have two journal ent

eimsori [14]

There are two different ways she can write on her pages.
1) With one journal entry
2) With two journal entries

$10*2 \\ 20$

There are twenty different ways she can write them in her journal.

7 0

3 years ago

What is the solution to the following equation? x2 + 3x + 4 = 0​

What is the solution to the following equation? x2 + 3x + 4 = 0