Question

Quadratic

3p^2−7p−1=0

Answer 1

x = 7 + √61 ÷ 6

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

Answer 2

`x=(7\pm√(61) )/(6)`

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:
  `x=(-b\pm√(b^2-4ac) )/(2a)`

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]:
   `x=(7\pm√((-7)^2-4(3)(-1)) )/(2(3))`
2. Evaluate Exponents:
   `x=(7\pm√(49-4(3)(-1)) )/(2(3))`
3. Multiply:
   `x=(7\pm√(49+12) )/(6)`
4. Add:
   `x=(7\pm√(61) )/(6)`