Find the root of the following quadratic equations, if they exist, by using the quadratic formula by Shridharacharya Method:

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

ax² + bx + c = 0

a = √2

b = 7

c = 5√2

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

⟹ (7)² – (4 × √2 × 5√2)

⟹ 49 – (20 × 2)

⟹ 49 – 40

⟹ 9

Since b² – 4ac = 121 the roots are real and distinct.

Now let us put the values in the above formula

Solving with positive value first,

x = -√2

Solving with negative value second,