1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
luda_lava [24]
3 years ago
11

Explain the difference between quadratic equations with one solution, two solutions, and complex solutions

Mathematics
1 answer:
shusha [124]3 years ago
4 0
Recall that given the equation of the second degree (or quadratic)
 ax ^ 2 + bx + c
 Its solutions are:
 x = (- b +/- root (b ^ 2-4ac)) / 2a
 discriminating: 
 d = root (b ^ 2-4ac)
 If d> 0, then the two roots are real (the radicand of the formula is positive). 
 If d = 0, then the root of the formula is 0 and, therefore, there is only one solution that is real and of multiplicity 2 (it is a double root).
 If d <0, then the two roots are complex and, in addition, one is the conjugate of the other. That is, if one solution is x1 = a + bi, then the other solution is x2 = a-bi (we are assuming that a, b, c are real).
 One solution:
 A cut point with the x axis
 Two solutions:
 Two cutting points with the x axis.
 Complex solutions:
 Does not cut to the x axis
You might be interested in
What is the angle of rotation of the figure?
tamaranim1 [39]
The rotation is were you keep one point at the same spot and move the others
5 0
3 years ago
Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with
skad [1K]

Parameterize S by the vector function

\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle

The integral of the field over S is then

\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv

\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv

\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}

8 0
2 years ago
Please answer correctly, im giving 45 points and brainliest. You get like 25 points
Aleonysh [2.5K]

c. Roller Rink F charges 1.00 more per person than roller rink G.

5 0
3 years ago
An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. The area of the trapezoid is
Mice21 [21]

Answer:

Option A is correct.      

Step-by-step explanation:

Given an isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. we have to find the area of isosceles trapezoid.

An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14.

From the figure attached , we can see an isosceles trapezoid ABCD,

AB = 8cm and CD=14cm

So we have to find the value of AE which is the height of Trapezoid in order to find area.

In ΔAED

tan\angle 45 =\frac{AE}{ED}

⇒ AE=1\times 3

∴ AE = DE =3cm

\text{The area of the trapezoid=}\frac{h}{2}\times (a+b)

h=3cm, a=14cm, b=8cm

Area=\frac{3}{2}\times(14+8)=\frac{3}{2}\times 22=33 units^2

hence, \text{The area of the trapezoid is }33 units^2

Option A is correct.

3 0
3 years ago
Read 2 more answers
Help! giving 13 points!
Shtirlitz [24]
To determine the perimeter of the triangle given the vertices, calculate the distances between pair of points. For the first pair (-5,1) and (1,1), the distance is 6. For the next pair, (1,1) and (1, -7), the distance is 8. Lastly, for the pair of points (-5,1) and (1, -7), the distance is 10. Adding all the distance will give the perimeter of the triangle. Thus, the perimeter is 24. 
6 0
3 years ago
Other questions:
  • I need help help on 4 please
    13·1 answer
  • Can someone PLEASE answer this question (picture above)
    13·1 answer
  • Any number raised to the power of zero is zero true or false
    14·2 answers
  • 3/8 (c+8) = -3/2 I need help with this
    14·1 answer
  • Suppose you invest $1,600 at an annual interest rate of 4.6% compounded continuously how much will you have in the account after
    7·1 answer
  • Twenty percent of candies in a package are red. The rest are another color.
    14·2 answers
  • In each of the following expressions, c represents the original cost of an item
    9·1 answer
  • A climber is descending at a rate of 345 feet per hour. What is the climber's change in altitude after three hours of climbing?​
    10·1 answer
  • F (x)= -3x+10 and g (x) = x^2-7x<br> f(-5)=<br> g(2)=<br> f(4m)=
    13·1 answer
  • What is the distance between the points (59.5, 34.2) and (15.3, 14.9)? Enter your answer rounded to the nearest tenth (0.1).
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!