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
(1 + 7m)(4) what is it simplified
jek_recluse [69]
Answer
4+21m
Explanation
Use the distributive property 4 times 1 and 4 times 7m keep the m
4 0
3 years ago
How many solutions are there to the following system of equations?
sweet [91]
4x-8y=0 \\&#10;\underline{-3x+8y=-7} \\&#10;4x-3x=0-7 \\&#10;x=-7 \\ \\&#10;4x-8y=0 \\&#10;4 \times (-7)-8y=0 \\&#10;-28-8y=0 \\&#10;-8y=28 \\&#10;y=\frac{28}{-8} \\&#10;y=-\frac{7}{2} \\ \\&#10; \left \{ {{x=-7} \atop {y=-\frac{7}{2}}} \right.

There is one solution to this system of equations. The answer is B.
6 0
3 years ago
Read 2 more answers
Vidriana rolled a number cube 96 times. Her results are shown in the table, what is the experimental probability of rolling an e
hichkok12 [17]

Answer:

50/96

Step-by-step explanation:

I assume the table is:

\left[\begin{array}{cc}Result&Total\\1&15\\2&13\\3&16\\4&17\\5&15\\6&20\end{array}\right]

Even numbers are 2, 4, and 6.  The total number of times she rolled an even number is 13 + 17 + 20 = 50.

So the probability is 50/96.

7 0
3 years ago
Given the system of equations presented here:
Bumek [7]

ANSWER

The correct answer is option B

EXPLANATION


The equations are

3x+5y=29---(1)


and


x+4y=16---(2)


When we multiply the second equation by -3, we obtain;


-3x-12y=-48---(3)


When we combine this new equation with equation (1).


-7y=-19


We can see that x has been eliminated from the equation.


We can then, solve for  y and then substitute the result in to any of the equations to find x.


Hence the correct answer is option B



8 0
3 years ago
Read 2 more answers
HELPPPPPPP ASAPPPPP<br> Match each graph with the logarithmic function it represents.
OverLord2011 [107]

Answer:

f(x)=3-4 In (x-2)=graph 3

f(x)=3-In x=graph 1

f(x)=In (x+1)=graph 4

f(x)= 2In (x+3)= graph 2

Step-by-step explanation:

Use a graph tool to visualize the functions.Attached are the graphed functions respectively.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone help me!! I’m trying to find equivalent measures! 15!points if you can help!
    10·1 answer
  • PLease help mee with these math questions, please.
    15·1 answer
  • 9w-4w+6&lt;1+5w supposed to combine like terms
    9·1 answer
  • How do you do this mathematics problem D-3/5=5/8
    15·1 answer
  • What is the factor to change pounds to kilograms
    11·1 answer
  • Can someone please help me solve this<br> 20 points to the person who can help me solve
    14·1 answer
  • The number of students who ordered a medium T-shirt was two less than
    12·2 answers
  • <img src="https://tex.z-dn.net/?f=%5Csf%2016%2B11%5Ctimes%209" id="TexFormula1" title="\sf 16+11\times 9" alt="\sf 16+11\times 9
    15·1 answer
  • the EM wave emitted by the sun and responsible for heating the Earths atmosphere due to green house effect is
    14·1 answer
  • Select the correct solution for the expression. 2/5 + 3/8
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!