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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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