Q.Using Sridharacharya's formula, solve $3x^2 - 5x - 2 = 0$.

Identify $a=3, b=-5, c=-2$ and substitute directly into the formula.

General form gives $a=3, b=-5, c=-2$.

Compute the discriminant: $D = b^2-4ac = (-5)^2 - 4(3)(-2) = 25+24 = 49$.

Since $D=49>0$, the equation has two distinct real roots.

Apply Sridharacharya's formula: $x=\dfrac{-b\pm\sqrt D}{2a}=\dfrac{5\pm\sqrt{49}}{6}=\dfrac{5\pm7}{6}$.

Taking the $+$ sign: $x=\dfrac{12}{6}=2$. Taking the $-$ sign: $x=\dfrac{-2}{6}=-\dfrac13$. …

Alternative — factorization: $ac=3\times(-2)=-6$; need $p,q$ with product $-6$, sum $-5$: $p=-6,q=1$. $3x^2-6x+x-2=0 \Rightarrow 3x(x-2)+1(x-2)=0 \Ri …

The most common error with Sridharacharya's formula is a sign slip on $-4ac$ when $c$ is itself negative — here $-4ac=-4(3)(-2)=+24$, a double-negative that students often mishandle as $-24$. Always compu …