Math, asked by techiangung642, 11 months ago

What do you mean by Dharachaarya Formula

Answers

Answered by radheshyam15761
0

Answer:

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

Answered by Anonymous
5

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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}

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