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
posledela
3 years ago
8

Does the parabola with equation x2 – x + 4 = 0 have real or imaginary roots?

Mathematics
2 answers:
Harman [31]3 years ago
8 0
4. If the determinant delta of a quadratic equation is positive, the equation has two real roots. If the determinant is negative, it has two imaginary roots. In this case, delta=b^2-4ac=(-1)^2-4*1*4=-15. Therefore, this equation has two imaginary roots.
adoni [48]3 years ago
6 0

Answer:

The parabola with equation x^2\:-\:x\:+\:4\:=\:0 has two imaginary roots, because the discriminant is negative.

Step-by-step explanation:

The quadratic formula says that the solutions are

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

for any quadratic equation like:

                                                   ax^2+bx+c=0

The discriminant is the part of the quadratic formula under the square root.

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.

  • A positive discriminant indicates that the quadratic has two distinct real number solutions.
  • A discriminant of zero indicates that the quadratic has a repeated real number solution.
  • A negative discriminant indicates that neither of the solutions are real numbers but there are two imaginary roots that are complex conjugates.

We have the parabola with equation x^2\:-\:x\:+\:4\:=\:0

\mathrm{For\:}\quad a=1,\:b=-1,\:c=4:\quad x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:4}}{2\cdot \:1}

The discriminant for this equation is \sqrt{\left(-1\right)^2-4\cdot \:\:1\cdot \:\:4}= \sqrt{-15}, because the discriminant is negative the parabola has two imaginary roots.

You might be interested in
PLEASEEE HELP FAST
Viktor [21]

Answer:

1. 4 as that is when he is closest.

2. 3 is when he is waiting as the graph is horizontal showing no movement

3. 4 would change as that is showing his pace walking home if it increased the slope would become steep but if it decreased it would level out more.

Step-by-step explanation:

4 0
3 years ago
A shoe box in the shape of a right rectangular prism has a base that measures 7 inches by 12 inches and is 5 inches high. What i
AlekseyPX

Answer:

The volume of the shoe box is 420 cubic inch

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a righ rectangular prism

Given data

Length of prism l= 12inches

Width of prism w= 7 inches

Height of prism h= 5 inches

We know that the volume of a rectangular prism is expressed as

Volume =l*w*h

Volume = 12*7*5= 420in³

6 0
3 years ago
Read 2 more answers
Find the size of angle XZY<br> Answer given to one decimal place
barxatty [35]

Answer:

159cm

Step-by-step explanation:

Sum of all sides of triangles is 180

so, 15+6=21

then 180-21=159

4 0
2 years ago
Which set of sides will make a triangle
ElenaW [278]

Answer:

the third one 10 cm, 9cm 9cm

6 0
3 years ago
Find the critical points of the function f(x, y) = 8y2x − 8yx2 + 9xy. Determine whether they are local minima, local maxima, or
NARA [144]

Answer:

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

Step-by-step explanation:

The function is:

f(x,y) = 8\cdot y^{2}\cdot x -8\cdot y\cdot x^{2} + 9\cdot x \cdot y

The partial derivatives of the function are included below:

\frac{\partial f}{\partial x} = 8\cdot y^{2}-16\cdot y\cdot x+9\cdot y

\frac{\partial f}{\partial x} = y \cdot (8\cdot y -16\cdot x + 9)

\frac{\partial f}{\partial y} = 16\cdot y \cdot x - 8 \cdot x^{2} + 9\cdot x

\frac{\partial f}{\partial y} = x \cdot (16\cdot y - 8\cdot x + 9)

Local minima, local maxima and saddle points are determined by equalizing  both partial derivatives to zero.

y \cdot (8\cdot y -16\cdot x + 9) = 0

x \cdot (16\cdot y - 8\cdot x + 9) = 0

It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:

\left \{ {{-16\cdot x + 8\cdot y=-9} \atop {-8\cdot x + 16\cdot y=-9}} \right.

The solution of the system is (3/8, -3/8).

Let assume that y = 0, the nonlinear system is reduced to a sole expression:

x\cdot (-8\cdot x + 9) = 0

Another solution is (9/8,0).

Now, let consider that x = 0, the nonlinear system is now reduced to this:

y\cdot (8\cdot y+9) = 0

Another solution is (0, -9/8).

The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:

H = \frac{\partial^{2} f}{\partial x^{2}} \cdot \frac{\partial^{2} f}{\partial y^{2}} - \frac{\partial^{2} f}{\partial x \partial y}

The second derivatives of the function are:

\frac{\partial^{2} f}{\partial x^{2}} = 0

\frac{\partial^{2} f}{\partial y^{2}} = 0

\frac{\partial^{2} f}{\partial x \partial y} = 16\cdot y -16\cdot x + 9

Then, the expression is simplified to this and each point is tested:

H = -16\cdot y +16\cdot x -9

S1: (0,0)

H = -9 (Saddle Point)

S2: (3/8,-3/8)

H = 3 (Local maximum or minimum)

S3: (9/8, 0)

H = 9 (Local maximum or minimum)

S4: (0, - 9/8)

H = 9 (Local maximum or minimum)

Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:

S2: (3/8,-3/8)

f(\frac{3}{8} ,-\frac{3}{8} ) = - \frac{27}{64} (Local minimum)

S3: (9/8, 0)

f(\frac{9}{8},0) = 0 (Local maximum)

S4: (0, - 9/8)

f(0,-\frac{9}{8} ) = 0 (Local maximum)

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

4 0
3 years ago
Other questions:
  • Simplify. (3x5+3x2−4x3+x−6)−(x3+4x4+2x2−10x) Enter your answer, in standard form, in the box.
    14·2 answers
  • Enter the number that belongs in the green box. <br><br> Please help!!!
    15·2 answers
  • What are the domain and range of f(x)=(1/5)x
    12·1 answer
  • If I have more 15 Pokemon cards than Austin, which expression shows how many |<br>have?​
    12·1 answer
  • Mr. Pham mowed 2/7 of his lawn. his son mowed 1/4 of the lawn who mowed the most? How much of the lawn still needs to be mowed
    12·2 answers
  • Please help!!
    9·2 answers
  • Hey , can you help me..?
    15·2 answers
  • Choose a way to solve.
    5·1 answer
  • Nikki can drive her car 22 miles on each gallon of gasoline. If Nikki drives m miles, which expression represents the number of
    13·2 answers
  • In the problem 7/10 – 3/4, what is the LCM you can use as the denominator in both fractions?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!