Solve the following quadratic equations by using Shridharacharya Quadratic Formula:

p²x² + (p² – q²)x – q² = 0

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

a = p²

b = (p² – q²)

c = – q²

There is one formula developed by Shridharacharya to determine the roots of a quadratic equation which is as follows:

Before putting the values in the formula let us check the nature of roots by b² – 4ac >0

⟹ ((p² – q²)) ² – (4 × p × – q²)

⟹ (p⁴ –2 p² q² + q⁴) - (-4p²q²)

⟹ p⁴ –2 p² q² + q⁴ + 4p²q²

⟹ (p⁴ + 2 p² q² + q⁴)

⟹ ((p² + q²)) ²

Now let us put the values in the above formula

Solving with positive value first,

x = q² / p²

Solving with negative value second,

x = -1