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
Tatiana [17]
3 years ago
5

Find the nature of the root

Mathematics
1 answer:
GREYUIT [131]3 years ago
6 0

Answer:

1) Real and same.

2) Real and distinct

3) Real and distinct

4) Real and distinct

5) Real and distinct

6) Real and distinct

7) Real and distinct

8) Real and distinct

Step-by-step explanation:

If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.

If D > 0, then there will be two different real roots.

If D = 0, then two same and real roots.

If D < 0, then two distinct but imaginary roots.

Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.

2) 5x² - x = 4x² + 2

⇒ x² - x - 2 = 0

It has D = (-1)² - 4 × 1 × (-2) = 9. Therefore, the roots will be two distinct and real.

3) \frac{2}{x} + \frac{3}{x} = x - 4

⇒ 5 = x² - 4x

⇒ x² - 4x - 5 = 0.

So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.

4) x(x - 5) = 4(5 - x)

⇒ x² - x - 20 = 0

Hence, D = (-1)² - 4 × 1 × (-20) = 81

So, the roots will be real and distinct.

5) x² + 7x + 1 = 0 has D = 7² - 4 × 1 × 1 = 45

So, the roots will be real and distinct.

6) 2x² + 9x + 3 = 0, has D = 9² - 4 × 2 × 3 = 57.

Hence, the roots will be real and distinct.

7) 5x² - 6 = 13x

⇒ 5x² - 13x - 6 = 0

So, D = (-13)² - 4 × 5 × (-6) = 289

So, the roots will be real and distinct.

8) x² - x = 3(x + 7)

⇒ x² - 4x - 21 = 0

It has D = (-4)² - 4 × 1 × (-21) = 100

So, the roots will be real and distinct. (Answer)

You might be interested in
Help me find the mean mode range median
pashok25 [27]

Answer:

Mean=2.53

median=2

mode=2

range=3

Step-by-step explanation:

1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4

MEAN

Add up all data values to get the sum

Count the number of values in your data set

Divide the sum by the count

38/15=2.53

MEDIAN

Arrange data values from lowest to the highest value

The median is the data value in the middle of the set

If there are 2 data values in the middle the median is the mean of those 2 values.

MODE

Mode is the value or values in the data set that occur most frequently.

RANGE

18-15=3

5 0
3 years ago
Rectangle
Viefleur [7K]

Answer:

  21 square units

Step-by-step explanation:

The sides of the rectangle are aligned with the coordinate grid, so we can easily find its dimensions.

AB lies on the line y = -2, so the horizontal extent is the difference in x-values:

  6 - 3 = 3

BC lies on the line x = 6, so the vertical extent is the difference in y-values:

  5 -(-2) = 7

The area is the product of these two dimensions:

  A = LW = (7)(3) = 21 . . . . square units

The area of the rectangle is 21 square units.

3 0
2 years ago
Read 2 more answers
What is the slope of the line x=5
Andre45 [30]
The slope would go vertically starting it at 5. you place your dot at 5 and draw a line going up and down throughout both the top and bottom of the right side of the graph. hope it helped
5 0
3 years ago
If a person walks 2.4 miles in i.5hours how far can he walk in 3hours
Lubov Fominskaja [6]
I used the cross product method
5x = 2.4 •3
5x=7.2
7.2divided by 5
1.44 miles in 3 hours

Hope I helped
8 0
2 years ago
Rule: start at 17.3 add 0.9 please help
ra1l [238]
17.3, 18.2, 19.1, 20
6 0
3 years ago
Other questions:
  • 64% of 75 tiles is?
    9·2 answers
  • In the equation Y+8=2 what does y=?
    6·1 answer
  • If Jackie were to paint her living room alone it would take five hours. Her sister Violet could do the job in six hours. How lon
    15·1 answer
  • Which of the following is a type of face found on a Platonic solid
    14·2 answers
  • What is the value of X? show all of your work
    6·1 answer
  • Use place value to find the product 6x40
    6·1 answer
  • HELP!!! Gracie read 150 pages of a book she got for her birthday. The book is 227 pages long. Which equation shows how to find t
    9·1 answer
  • The bill for your dinner was $12 and you paid $4 gratuity. What percent gratuity did you<br> give?
    15·1 answer
  • How Do i find slope ?
    6·2 answers
  • Two supporting reasons are missing from the proof. Complete the proof by dragging and dropping the appropriate reasons into each
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!