Question

Derive quadratic formula

Answer 1

Answer:

Hey dude!!!

Derivation of Quadratic Formula:-

1) Divide both sides of the equation

$a {x}^{2} + bx + c = 0 \: by \: a$

2) Transpose the quantity c/a to the right side of the equation.

3) Complete the square by adding {b} ^{2} / 4{a}^{2} to both sides of the equation.

4) Factor the left side and combine the right side.

5) Extract the square-root of both sides of the equation.

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Answer 2

Answer:

Derivation of quadratic formula

let us take an example: ax ^ 2 + bx + c = 0

step 1 : complete the square

ax^ 2 + bx + c in this X is two tyms

start it ::::: ax^ 2 + bx + c = 0

divide the eq by a

::::::ax ^ 2 / a + bx / a + c / a = 0

:::::::::X ^ 2 + bx / a + c / a = 0

put c / a on the other side

::::::::x ^ 2 + b x / a = - c / a

add (b / 2a )^ 2 on both side

::::::: x ^ 2 + b x / a +( b / 2a )^ 2 = - c / a + (b /2a )^2

complete the square

::::: (x + b / 2a )^ 2 = - c / a + ( b / 2a ) ^ 2

::::::: make square root on other side

:::::::::x + b / 2a = √ - c / a + ( b / 2a ) ^ 2

move b / 2a in the right side

x = - b / 2a + √ - c / a + ( b / 2a ) ^ 2

multiply right by 2a / 2a

X = - b / 2a + √ - c / a× 2a + ( b / 2a ) ^ 2 × 2a

= - b +- √ - 4ac + b ^ 2

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2a

it's solved .hope u like it