Sridharacharya's Method (Statement)

Sridharacharya's rule gives the roots of $ax^2+bx+c=0$ ($a \neq 0$) directly, as a formula, without repeating the completing-the-square steps each time:

This chapter uses the formula by statement only — the syllabus explicitly does not require its derivation or proof; §4's perfect-square method is the derivation route for a student who wants to see where it comes from, but examinations at this level expect direct application of the boxed formula above.

How to apply it:

1. Write the equation in general form $ax^2+bx+c=0$ and read off $a$, $b$, $c$ (with their correct signs).
2. Substitute into the formula and compute $b^2 - 4ac$ first (this quantity is called the discriminant, studied in detail in §6).
3. Take the square root of the discriminant, then apply both the $+$ and $-$ signs to get the two roots $x_1$ and $x_2$ (which coincide into one repeated root when the discriminant is exactly zero).