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
Sergeeva-Olga [200]
3 years ago
11

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

ed. x^2 + 5x + 4 = 0

Mathematics
1 answer:
zavuch27 [327]3 years ago
5 0

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

You might be interested in
What can you conclude about triangle 2?
Lemur [1.5K]

Answer: Triangle 2 is congruent to triangle 1 because a translation is a rigid motion

Step-by-step explanation:

8 0
3 years ago
Simplify the expression:<br><br> 4(9p + 1)
Tju [1.3M]

Answer:

36p+4

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Find the value of x that solves the system shown below.<br> y = 5x<br> 2x - y = 18
cestrela7 [59]
Since 5x is equal to y.we can write 5x instead of y in the equation.and then solve the equation

7 0
3 years ago
You are still debating about the two different computers. If you are paid $10.00/hour and your deductions are FICA (7.65%), fede
sattari [20]

Answer:

89 hours

Step-by-step explanation:

First solve all the deductions.

For each multiply the $10, which you are paid, and the percentage.

For FICA: $10 x 0.0765 = $0.77 per hr

For Fed tax: $10 x 0.12 = $1.2 per hr

For State tax: $10  x 0.08 = $0.8 per hr

Now subtract the remaining pay:

10 – 0.77 – 1.2 – 0.8 = $7.23

Time required = $640 / $7.23 per hr

Time required = 89 hrs

Final answer:

89 hours

8 0
3 years ago
Tracy brought 5 trays of plants for $105. Each tray contained 12 plants. Each plant cost the same amount. Plants can be purchase
KiRa [710]
131.25 but she would spend 26.25 more
4 0
3 years ago
Read 2 more answers
Other questions:
  • A 2-column table with 4 rows. Column 1 is labeled Store with entries A, B, C, D. Column 2 is labeled Advertised Bread Prices wit
    15·1 answer
  • Solutions of x2 + 13x + 30 = 0 by factoring.
    14·1 answer
  • 3 packets of French fries, 2 cheeseburgers, and one drink cost $10.95. 1 packet of French fries, 2 cheeseburgers, and 3 drinks c
    7·1 answer
  • I need to know this asap!
    10·1 answer
  • At a restaurant Mike and his three friends decided to divide the bill evenly if each person pay $13 then what was the total bill
    7·2 answers
  • Isabella collected 1/4 gallon of honey from her beehive. She wants to fill her jar, which holds 3/10 gallon. What fraction of he
    13·1 answer
  • What is 7/8 days in hours​
    8·1 answer
  • Can i get some help please -2v(1-7v)+v-10
    5·1 answer
  • From the information in the diagram, what is H
    11·1 answer
  • Please help me aspa <br><br><br><br><br><br>​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!