Respuesta :

Space

Answer:

[tex]x=\frac{7\pm\sqrt{61} }{6}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

  • Standard Form: ax² + bx + c = 0
  • Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

Step 1: Define

3p² - 7p - 1 = 0

Step 2: Identify Variables

a = 3

b = -7

c = -1

Step 3: Find roots

  1. Substitute [Quad Formula]:                   [tex]x=\frac{7\pm\sqrt{(-7)^2-4(3)(-1)} }{2(3)}[/tex]
  2. Evaluate Exponents:                              [tex]x=\frac{7\pm\sqrt{49-4(3)(-1)} }{2(3)}[/tex]
  3. Multiply:                                                  [tex]x=\frac{7\pm\sqrt{49+12} }{6}[/tex]
  4. Add:                                                        [tex]x=\frac{7\pm\sqrt{61} }{6}[/tex]
TheUnknownScientist

Answer:

x = 7 + √61 ÷ 6

Step-by-step explanation:

3p² - 7p - 1 = 0 is a given equation

3p² - 7p - 1 = 0

Here,

a = 3

b = - 7

c = - 1

Now, Discriminant

D = b² - 4ac

= (- 7)² - 4 (3)(- 1)

= 49 + 12

D = 61 > 0

So, Quadratic Equation

ax² + bx + c = 0

x = - b ± √b² - 4ac ÷ 2a

x = - (- 7) ± √(- 7)² - 4 (3)(- 1) ÷ 2(3)

x = 7 ± √61 ÷ 6

x = 7 ± √61 ÷ 6

x = 7 + √61 ÷ 6 or x = 7 - √61 ÷ 6

∴ Not real Value

Thus, The real value of x is 7 + √61 ÷ 6

-TheUnknownScientist

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