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
ella [17]
2 years ago
6

Find the roots of the quadratic equation x^2 + 7x + 10 = 0 by using the quadratic formula​

Mathematics
2 answers:
Mila [183]2 years ago
8 0

Hey there!

  • Answer :
  • x = -5 or x = -2 ✅

  • Explanation :

<em><u>QUADRATIC EQUATION:</u></em>

ax² + bx + c = 0 where a ≠ 0

The sign of the discrimant (b² - 4ac) determines the number of real-number solutions :

  • If the discrimant is positive, the equation has <em><u>two real-number solutions</u></em>.
  • If the discrimant is equal to zero, the equation <em><u>has one real-number solution</u></em>.
  • If the discriminant is negative, the equation has <em><u>no real-number solution</u></em>.

The solutions of the equation, also called roots, can be obtained with the QUADRATIC FORMULA :

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

---------------------------------------------------------------

▪️ x² + 7x + 10 = 0

(1) Substitute the letters in the general quadratic equation with their values in the given expression:

  • a = 1
  • b = 7
  • c = 10

(2) <em>Determine the sign of the discriminant: </em>

{b}^{2} - 4ac \\ \\ \Longrightarrow {7}^{2} - 4(1)(10) \\ \\ \Longrightarrow 49 - 40 \: \: \: \: \: \: \: \: \: \\ \\ \Longrightarrow \red{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

The discrimant is positive ; the equation has two real-number solutions.

(3) <em>Determine the roots of the equation :</em>

  • a)

x_1 = \frac{ - b \: - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_1 = \frac{ - 7 - \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = \frac{ - 7 - 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{10}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \green{ \boxed{ \red{x_1 = - 5}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

  • (b)

x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 7 + \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = \frac{ - 7 + 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{4}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \red{ \boxed{ \green{x_2 = - 2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

Therefore, x = -5 or x = -2

▪️ Learn more about quadratic equations :

↣brainly.com/question/3843409

sweet-ann [11.9K]2 years ago
4 0

Answer:

x = -2, -5

Step-by-step explanation:

x^2 + 7x + 10 = 0

The factors of 10 are as follows:

1, 10

2, 5

We can combine 2 and 5 to make 7

(x +2) (x + 5) = 0

One of these brackets must equal 0 to make the answer 0, as you are multiplying them together

If x + 2 = 0, x = -2

If x + 5 = 0, x = -5

Therefore, x = -2, -5

You might be interested in
Which equation describes a line of symmetry for the figure shown? x = 0 y=−x y = x y = 0
Katena32 [7]

Answer:

y=0

Step-by-step explanation:

Hope this helped!!!

6 0
3 years ago
Directions: Calculate the percent increase or decrease between the starting and ending
Sveta_85 [38]

I'll do the first two to get you started

===============================================

Problem 1

A = 3 = starting value

B = 10 = ending value

C = percent change

C = [ (B - A)/A ] * 100%

C = [ (10-3)/3 ] * 100%

C = (7/3) * 100%

C = 2.3333333 * 100%

C = 233.33333%

C = 233.3%

The positive C value means we have a percent increase. If C was negative, then we'd have a percent decrease.

<h3>Answer: 233.3% increase</h3>

===============================================

Problem 2

A = 9 = start value

B = 20 = end value

C = percent change

C = [ (B - A)/A ] * 100%

C = [ (20-9)/9 ] * 100%

C = (11/9)*100%

C = 1.2222222222*100%

C = 122.22222222%

C = 122.2%

<h3>Answer: 122.2% increase</h3>
7 0
3 years ago
Read 2 more answers
What did you guys get for all of these?<br> I’ll give you 30 points If you’re able to answer all.
alex41 [277]

Answer:

can u zoom in and take picture

Step-by-step explanation:

8 0
3 years ago
rail fares go up by 10%, and josie’s new season ticket to london costs £1342. calculate how much more she has to pay now than sh
Naya [18.7K]

Answer:

£134.2 more

Step-by-step explanation:

Divide 1342 by 100

Then you get 13.42

Times that by 10 and £134.2 is 10%

6 0
2 years ago
What is the line of symmetry for the parabola whose equation is y = -x2 + x + 3?
iVinArrow [24]
Alright so if I do remember my math correctly, this is how it goes:

- y = -x^2 + x + 3

- x = -b/2a

- x = -1/2(-1)

- x = -1/-2, which = (1/2)

Not quite sure if this was correct, but if it was, hope this helps and you're welcome! :)
5 0
3 years ago
Read 2 more answers
Other questions:
  • Tiana can clear a football feild of debris in 3 hours. Jacob can clear the same feild in 2 hours. If they decide to clear the fe
    6·1 answer
  • A golfer hits a ball from a starting elevation of 2 feet with a velocity of 70 feet per second down to a green with an elevation
    14·1 answer
  • Can someone please tell me how to solve this?
    9·1 answer
  • Sally read 13 books during this month. her brother read 7 books. one fourth out of all books they read were non fiction. how man
    12·1 answer
  • How do I round it if technically it’s already to the nearest hundredth
    5·1 answer
  • Write 4x5 3/8 as a mixed number
    14·1 answer
  • Enter the value, as a mixed number in simplest form, in the box. |2 1/3| = ?
    13·1 answer
  • Andy had some basketball cards. After he bought 12 more, he had 48 cards. How many cards did Andy have at the start? Write an al
    11·1 answer
  • What is 2/5 × 5/6 in simplist form
    5·1 answer
  • I need to find the value of x​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!