Question

Find the discriminant of x2-6x -10 = 0, and determine the number of real solutions of the equation.​

Answer 1

76

2 real solutions

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

Discriminant: b² - 4ac

• Positive - 2 solutions
• Equal to 0 - 1 solution
• Negative - No solutions/Imaginary

Explanation:

Step 1: Define

x² - 6x - 10 = 0

Step 2: Identify Variables

Compare quadratic.

x² - 6x - 10 = 0 ↔ ax² + bx + c = 0

a = 1, b = -6, c = -10

Step 3: Find Discriminant

1. Substitute in variables [Discriminant]: (-6)² - 4(1)(-10)
2. [Discriminant] Evaluate exponents: 36 - 4(1)(-10)
3. [Discriminant] Multiply: 36 + 40
4. [Discriminant] Add: 76

This tells us that our quadratic has 2 real solutions.