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Which of the following are solutions to the equation below? Check all that apply. 2x2 + 18 x = 20 A. 20 I B. 1 C. -2 O D. -2 E. -10 1 F. -1​

Which of the following are solutions to the equation below Check all that apply 2x2 18 x 20 A 20 I B 1 C 2 O D 2 E 10 1 F 1 class=

Respuesta :

Answer:

B and E

Step-by-step explanation:

To verify which are solutions, substitute the given values into the left side of the equation and if equal to the right side then they are solutions.

A

2(20)² + 18(20) = 800 + 360 = 1160 ≠ 20 ← not a solution

B

2(1)² + 18(1) = 2 + 18 = 20 ← solution

C

2(- 2)² + 18(- 2) = 2(4) - 36 = 8 - 36 = - 28 ≠ 20 ← not a solution

D

Is a repeat of C

E

2(- 10)² + 18(- 10) = 2(100) - 180 = 200 - 180 = 20 ← solution

F

2(- 1)² + 18(- 1) = 2(1) - 18 = 2 - 18 = - 16 ≈ 20 ← not a solution

Then B and E are solutions to the equation

[tex] \huge \mathrm{Answer࿐ }[/tex]

let's solve the quadratic equation :

  • [tex]2 {x}^{2} + 18x = 20[/tex]

  • [tex]2 {x}^{2} + 18x - 20 = 0[/tex]

  • [tex]2 {x}^{2} + 20x -2 x - 20 = 0[/tex]

  • [tex]2x(x + 10) - 2(x + 10) = 0[/tex]

  • [tex](2x - 2)(x + 10) = 0[/tex]

So, there are two cases :

Case - 1 (when, 2x - 2 = 0)

  • [tex]2x - 2 = 0[/tex]

  • [tex]2x = 2[/tex]

  • [tex]x = 1[/tex]

Case - 2 (when, x + 10 = 0)

  • [tex]x + 10 = 0[/tex]

  • [tex]x = - 10[/tex]

Therefore the required options will be :

  • B. 1 and E. -10

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