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Differences and similarities

Chalana-Kalanabhyam

This sutra solves simple quadratic equations of the form x² - Sx + P = 0 by finding two numbers that multiply to give the constant term (P) and add to give the middle coefficient (S). Once found, those two numbers are the roots.

How It Works

  1. 1.Start with a quadratic equation x² - Sx + P = 0.
  2. 2.Identify S (sum of roots) and P (product of roots).
  3. 3.List factor pairs of P: find all pairs (a, b) where a × b = P.
  4. 4.Check which pair adds up to S: a + b = S.
  5. 5.The two numbers are the roots: x = a and x = b.

Examples

x² − 7x + 12 = 0
Step 1 / 4

Start with x² − 7x + 12 = 0. Identify the sum (S) and product (P) of roots.

Equationx² − 7x + 12 = 0
Sum (S)7
Product (P)12

Try It Yourself

x² − 10x + 21 = 0 → smaller root?

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