All categories

2 years ago

Solving quadratic equations with complex solutions x2 + 4x + 8 = 0.

Mathematics

1 answer:

Daniel [21]2 years ago

4 0

Answer:

$\large\boxed{x=-2\pm2i}$

Step-by-step explanation:

$x^2+4x+8=0\qquad\text{subtract 8 from both sides}\\\\x^2+4x+8-8=0-8\\\\x^2+2(x)(2)=-8\qquad\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2(x)(2)+2^2=-8+2^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=-8+4\\\\(x+2)^2=-4\iff x+2=\pm\sqrt{-4}\\\\x+2=\pm\sqrt{(4)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x+2=\pm\sqrt4\cdot\sqrt{-1}\qquad\text{use}\ \sqrt{-1}=i\\\\x+2=\pm2\cdot i\qquad\text{subtract 2 from both sides}\\\\x=-2\pm2i$

You might be interested in

Can someone help me find the equation for this line please

pogonyaev

Answer:

y = x + 1

Step-by-step explanation:

The line y = x goes through the origin, and forms a perfect 45 degree angle with the x axis.

This is that same line, moved upward 1 unit, so the y value comes out 1 unit more.

Also, in y = mx + b form (slope-intercept form), we see slope m = 1 and y-intercept b = 1, so

y = 1x + 1 = x + 1

y = x + 1

5 0

2 years ago

_ 1)

Alina [70]

Answer: A)

Step-by-step explanation: If You just look at the numbers you can single out which one is correct

3 0

3 years ago

Please help.... fast

zloy xaker [14]

Answer:

Step-by-step explanation:

It tells you the triangle is a right triangle and it tells you that the hypotenuse of both triangles is congruent.

I'm confident that this is the answer.

8 0

2 years ago

In the previous part, we obtained dy dx = 3t2 − 27 −2t . Next, find the points where the tangent to the curve is horizontal. (En

mina [271]

Answer:

(27.55, 7.22), (-11.3, 3.21).

Step-by-step explanation:

When is the tangent to the curve horizontal?

The tangent curve is horizontal when the derivative is zero.

The derivative is:

$\frac{dy}{dx} = 3t^{2} - 2t - 27$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$3t^{2} - 2t - 27 = 0$

$a = 3, b = -2, c = -27$

Then

$\bigtriangleup = b^{2} - 4ac = (-2)^{2} - 4*3*(-27) = 328$

$t_{1} = \frac{-(-2) + \sqrt{328}}{2*3} = 3.35$

$t_{2} = \frac{-(-2) - \sqrt{328}}{2*3} = -2.685$

Enter your answers as a comma-separated list of ordered pairs.

We found values of t, now we have to replace in the equations for x and y.

t = 3.35

$x = t^{3} - 3t = (3.35)^{3} - 3*3.35 = 27.55$

$y = t^{2} - 4 = (3.35)^2 - 4 = 7.22$

The first point is (27.55, 7.22)

t = -2.685

$x = t^{3} - 3t = (-2.685)^3 - 3*(-2.685) = -11.3$

$y = t^{2} - 4 = (-2.685)^2 - 4 = 3.21$

The second point is (-11.3, 3.21).

8 0

3 years ago

Enter the explicit rule for the geometric sequence.

Sveta_85 [38]

Answer: $\frac{3}{2}$ $(\frac{1}{2})^{n-1}$

<u>Step-by-step explanation:</u>

$\frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, ...$

common ratio (r) = $\frac{1}{2}$

first term (a₁) = $\frac{3}{2}$

$a_{n}$ = a₁ (r)ⁿ⁻¹

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

4 0

3 years ago