Quadratic Equations
Find roots instantly using Sutras.
Core Concepts
A quadratic equation looks like ax² + bx + c = 0. The goal is to find values of x (called roots) that make the equation zero.
The Factor Trick
For x² + 5x + 6 = 0:
Find two numbers that multiply to 6 and add to 5.
They are 2 and 3.
So factors are (x+2)(x+3).
Finding Roots
If factors are (x+2) and (x+3), just flip the signs!
Roots are -2 and -3.
"If (x-4) is a factor, x=4 is a root."
Solved Examples
Example 1: x² + 5x + 6 = 0
Question: Find roots.
• Product = 6, Sum = 5.
• Numbers are 2 and 3.
• Factors: (x+2)(x+3).
• Roots: -2, -3.
Example 2: x² - 5x + 6 = 0
Question: Find roots.
• Product = 6, Sum = -5.
• Numbers are -2 and -3.
• Factors: (x-2)(x-3).
• Roots: 2, 3.
Example 3: x² - 9 = 0
Question: Find roots.
• This is x² = 9.
• Square root of 9 is 3.
• Roots: 3, -3.
Example 4: (x-5)(x+1) = 0
Question: Find roots.
• If x-5 = 0, then x = 5.
• If x+1 = 0, then x = -1.
• Roots: 5, -1.
