Sridharacharya Formula
Sridharacharya Formula is a mathematical formula that is used to solve quadratic equations. The Sridharacharya formula is commonly also known as the quadratic formula. Sridharacharya gave a method to solve the quadratic equations and hence it is named after the great mathematician and is called the Sridharacharya Formula.
Let us now explore the Sridharacharya Formula and its proof. We will solve some examples to study the application of the Sridharacharya Formula for a better understanding.
1.  What is Sridharacharya Formula? 
2.  Sridharacharya Equation 
3.  Sridharacharya Formula Proof 
4.  How to Apply Sridharacharya Method? 
5.  FAQs on Sridharacharya Formula 
What is Sridharacharya Formula?
Sridharacharya Formula is also known as the quadratic formula or Sridharacharya Method. Sridharacharya Method is used to find solutions to quadratic equations of the form ax^{2} + bx + c = 0, a ≠ 0 and is given by x = (b ± √(b^{2}  4ac)) / 2a. It is named after the famous mathematician Sridharacharya who derived the Sridharacharya Method. It is one of the main math formulas. Quadratic equations can be solved using different methods such as factorization method, Sridharacharya formula (also known as the quadratic formula).
Sridharacharya Equation
The Sridharacharya formula is used to solve the Sridharacharya equation (also known as the quadratic equation). The Sridharacharya equation is given by ax^{2} + bx + c = 0, where a, b, c are real numbers and a ≠ 0. The solution of the Sridharacharya equation is given by the Sridharacharya formula which is x = (b ± √(b^{2}  4ac)) / 2a.
Sridharacharya Formula Proof
Now that we know that the Sridharacharya Formula is x = (b ± √(b^{2}  4ac)) / 2a which gives the solution of the Sridharacharya equation ax^{2} + bx + c = 0. We will derive the formula for Sridharacharya method using fundamental operations of math. We have,
ax^{2} + bx + c = 0
⇒ (1/a) ax^{2} + bx + c = (1/a)0 [Dividing both sides of the quadratic equation by a since a ≠ 0]
⇒ x^{2} + (b/a)x + (c/a) = 0
⇒ x^{2} + (b/a)x + (c/a)  (c/a) = (c/a) [Subtracting (c/a) from both sides of the equation]
⇒ x^{2} + (b/a)x = (c/a)
⇒ x^{2} + (b/a)x + b^{2}/4a^{2} = (c/a) + b^{2}/4a^{2 }[Completing squares by adding b^{2}/4a^{2} to both sides of the equation]
⇒ (x + b/2a)^{2} = (b^{2}  4ac)/4a^{2 }
⇒ (x + b/2a) = ± √(b^{2}  4ac)) / 2a [Taking square root on both sides]
⇒ x = b/2a ± (√(b^{2}  4ac)) / 2a [Subtracting b/2a from both sides of the equation]
⇒ x = (b ± √(b^{2}  4ac)) / 2a
Hence, we have derived the Sridharacharya Formula is x = (b ± √(b^{2}  4ac)) / 2a to determine the solution of the quadratic equation ax^{2} + bx + c = 0, a ≠ 0.
How to Apply Sridharacharya Method?
Now, we will study the application of the Sridharacharya Formula to solve a quadratic equation with the help of an example. Consider quadratic equation x^{2} + 4x + 3 = 0.
Here a = 1 , b = 4 and c = 3. After substituting the values into the Sridharacharya formula we have,
x = (4 ± √(4^{2}  4×1×3)) / 2 × 1
=(4 ± √(16  12 )) / 2
= (4 ± √4 ) / 2
=(4 ± 2 ) / 2
Now
x_{1} = (4 + 2) / 2
= 2/2 = 1
and x_{2} = (4  2) / 2
= 6/2
= 3
The roots of the quadratic equation x^{2} + 4x + 3 using the Sridharacharya method are 1 and 3.
Important Notes on Sridharacharya Formula:
 The Sridharacharya formula is commonly known as the Quadratic formula.
 Sridharacharya Method is used to find solutions to quadratic equations of the form ax^{2} + bx + c = 0, a ≠ 0.
 In case, a quadratic equation is not of the form ax^{2} + bx + c = 0, then we convert the equation to this standard form and then apply the Sridharacharya formula.
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Sridharacharya Formula Examples

Example 1: Solve the quadratic equation 2x^{2}  x  3 = 0 using the Sridharacharya Method.
Solution: As we compare the given quadratic equation 2x^{2}  x  3 = 0 with ax^{2} + bx + c = 0, we have a = 2, b = 1, c = 3.
Substituting the values of a, b, c into the Sridharacharya Formula, we have
x = ((1) ± √((1)^{2}  4×2×(3))) / 2 × 2
= [1 ± √(1+24)]/4
= [1 ± √25]/4
= (1 ± 5)/4
= 6/4, or 4/4
= 3/2 or 1
Answer: Hence the roots of quadratic equation 2x^{2}  x  3 = 0 are 3/2 and 1 using the Sridharacharya Formula.

Example 2: Determine the roots of the quadratic equation 5x^{2} + x = 0 using the Sridharacharya Formula.
Solution: As we compare the given quadratic equation 5x^{2} + x = 0 with ax^{2} + bx + c = 0, we have a = 5, b = 1, c = 0.
Substituting the values of a, b, c into the Sridharacharya Formula, we have
x = (1 ± √(1^{2}  4×2×0)) / 2 × 5
= [1 ± √(1  0)]/10
= [1 ± √1]/10
= (1 ± 1)/10
= 0/10, or 2/10
= 0 or 1/5
Answer: Hence the roots of quadratic equation 5x^{2} + x = 0 are 0 and 1/5 using the Sridharacharya Method.

Example 3: What is b^{2}  4ac in Sridharacharya Formula? What is its importance?
Solution:
The expression b^{2}  4ac in Sridharacharya Formula is known as discriminant. Since it is under the square root, we can use it to determine the number of solutions.
 If b^{2}  4ac > 0 then the roots are real and distinct.
 If b^{2}  4ac = 0 then the roots are real and equal.
 If b^{2}  4ac < 0 then the roots are imaginary and distinct.
 Answer: The importance of b^{2}  4ac is explained.
FAQs on Sridharacharya Formula
What is Sridharacharya Formula in Math?
Sridharacharya Formula is used to find solutions to quadratic equations of the form ax^{2} + bx + c = 0, a ≠ 0 and is given by x = (b ± √(b^{2}  4ac)) / 2a.
What is the famous name of the Sridharacharya formula?
The famous name of the Sridharacharya formula is the Quadratic formula.
Who invented the Sridharacharya formula?
The Sridharacharya formula was invented by a Bengali mathematician called the Sridhar Acharya.
What is the Sridharacharya Method?
Sridharacharya Method is a method that uses the Sridharacharya formula to solve quadratic equations.
What is the Use of the Sridharacharya Formula?
Sridharacharya Formula is used to find solutions to quadratic equations of the form ax^{2} + bx + c = 0, a ≠ 0
How to Use the Sridharacharya Formula?
To use the Sridharacharya Formula, compare the given quadratic equation with ax^{2} + bx + c = 0 and identify the values of a, b, c. After this, substitute these values of a, b, c into the formula of Sridharacharya method x = (b ± √(b^{2}  4ac)) / 2a to determine the roots of the equation.
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