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

76

2 real solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition 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

Step-by-step 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

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

This tells us that our quadratic has 2 real solutions.