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ella [17]
1 year ago
6

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

Mathematics
2 answers:
Mila [183]1 year 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]1 year 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

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BlackZzzverrR [31]
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Step-by-step explanation:

The cost of computer = $ 800

It losed 1/4th of value every year.

The value of computer after 0 years = cost of computer = $ 800

The value after 1 year = 800 - ( \frac{1}{4} (800)) = $600

The value after 2 years = 600 - ( \frac{1}{4} (600)) = $450

The value after 3 years = 450 - ( \frac{1}{4} (450)) = $337.5

The value after n years = computer cost at (n-1) year - \frac{1}{4} (n-1 cost)

7 0
3 years ago
Can someone pleasee help it’s quiz due rn
Free_Kalibri [48]

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Step-by-step explanation:

6 0
3 years ago
Sofia tem 52 triângulos retângulos isósceles iguais. Ela quer fazer quadrados usando alguns desses triângulos. Ela pode fazer qu
oee [108]

Answer:

Portanto, o Sofia pode fazer 6 tamanhos diferentes

Step-by-step explanation:

A fim de sermos capazes de determinar efetivamente quantos quadrados de diferentes tamanhos podem ser formados a partir do triângulo isósceles 52, resolvemos isso usando a fórmula

2 (n + 1) Onde n = 0 e todos os inteiros positivos

em outro para obter um tamanho diferente para os quadrados, temos que adicionar mais triângulos para aumentar o tamanho

a) quando n = 0

2 (0 + 1) = 2 × 1 = 2 triângulos isósceles iguais

A união de 2 triângulos isósceles forma um quadrado. Este é o primeiro quadrado

= 1 quadrado

b) quando n = 1

2 (1 + 1) = 2 × 2 = 4 triângulos isósceles iguais = 1 quadrado

c) quando n = 2

2 (2 + 1) = 2 × 3 = 6 triângulos isósceles iguais = 1 quadrado

d) quando n = 3

2 (3 + 1) = 2 × 4 = 8 triângulos isósceles iguais = 1 quadrado

e) quando n = 4

2 (4 + 1) = 2 × 5 = 10 triângulos isósceles iguais = 1 quadrado

f) quando n = 5

2 (5 + 1) = 2 × 6 = 12 triângulos isósceles iguais = 1 quadrado

Adicionamos o número total de triângulos usados

2 + 4 + 6 + 8 + 10 + 12 = 42 triângulos

42 triângulos de 52 triângulos formariam 6 quadrados com tamanhos diferentes

Vamos fazer mais um, onde n = 6

g) quando n = 6

2 (6 + 1) = 2 × 7 = 14 triângulos isósceles iguais = 1 quadrado

2 + 4 + 6 + 8 + 10 + 12 + 14 = 56 triângulos

Isso já excedeu o número dado de triângulos em questão.

Portanto, o Sofia pode fazer 6 tamanhos diferentes de quadrados usando 42 triângulos isósceles iguais

8 0
3 years ago
I need advice!
g100num [7]
Alright, so you can try to study hard and gain a passing grade (A+) for the other two quarters. 
4 0
3 years ago
Read 2 more answers
-5/4 = x -7/10 solve for x and show work please
tekilochka [14]
First lets start by making the denominators the same. I multiplied the 4 by 5 and 10 by 2.

-25/20 = x -14/20
Add 14/20 on both sides (do the opposite to cancel out and whatever you do to one side you need to do to the other.
You should get -11/20 = x
6 0
2 years ago
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