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

9x² + 7x – 2 = 0

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

ax² + bx + c = 0

a = 9

b = 7

c = -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 × 9 × -2)

⟹ 49 – (-72)

⟹ 49 + 72

⟹ 121

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 = 4 / 18

x = 2/9

Solving with negative value second,

x = -18 / 18

x = -1