पूर्वपरयोः
Pūrvaparayoh - “By the first and the last terms”
Solve quadratic equations by analyzing the first and last terms
What does it mean?
This Vedic Math sutra helps solve quadratic equations by focusing on the first and last terms of the trinomial expression.
It’s based on identifying two numbers whose product equals the last term and whose sum equals the middle term.
The Method
- Start with a quadratic equation:
-
x² + 5x + 6 = 0 - Identify first and last terms:
First: x², Last: +6 - Find two numbers whose product is 6 and sum is 5
- Choose the pair:
2 and 3 → 2×3 = 6, 2+3 = 5 - Write the factors:
(x + 2)(x + 3) = 0 - Solution:
x = -2, x = -3
Why it matters
This sutra offers a fast and intuitive way to factor quadratic equations without relying on lengthy formulas. It’s ideal for competitive exams and mental math, helping students solve problems in seconds by recognizing patterns in the first and last terms.