Question

What do you mean by Dharachaarya Formula

Answer 1

Answer:

the formula to find out roots of an quadratic equation which was given by Dharacharya.

Answer 2

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✯ Dharachaarya Formula :

Dharachaarya formula is also known as quadratic formula. Which is used to find the roots of an equation.

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✯ How to calculate Dharachaarya formula ?

Let the equation be : ax² + bx + c = 0

For finding the roots of equation.

Firstly, we have to calculate the value of D by discriminant method.

$\large{\boxed{\sf{D = b^2 - 4ac}}}$

After, finding the value of D we have to use one more formula to find the roots.

Which is given below :

$\large{\boxed{\sf{x = \frac{-b \pm \sqrt{D}}{2a}}}}$

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Now, Taking an example of equation : x² - 4x + 5 = 0

We know that,

$\large{\boxed{\sf{D = b^2 - 4ac}}}$

$\sf{\implies D = (4)^2 - 4(1)(-5)} \\ \\ \sf{\implies D = 16 -(-20)} \\ \\ \sf{\implies D = 16 + 20} \\ \\ \sf{\implies D = 36}$

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Now,

$\large{\boxed{\sf{x = \frac{-b \pm \sqrt{D}}{2a}}}}$

$\sf{\implies x = \frac{- 4\pm \sqrt{36}}{2(1)}} \\ \\ \sf{\implies x = \frac{-4 \pm 6}{2}}$

When positive

$\sf{\implies x = \frac{-4 + 6}{2}} \\ \\ \sf{\implies x = \frac{\cancel{2}}{\cancel{2}}} \\ \\ \sf{\implies x = 1}$

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When negative

$\sf{\implies x = \frac{-4 - 6}{2}} \\ \\ \sf{\implies x = \frac{-\cancel{10}}{\cancel{2}}} \\ \\ \sf{\implies x = -5}$