Derive Shreedharacharya quadratic formula .
Answers
Yes, you can!
Take the general quadratic function:
F(x) = ax^2 + bx + c
Now lets set F(x) to 0
ax^2 + bx + c = 0
And we move c across
ax^2 + bx = - c
and we divide throughout by a
x^2 + b/a x = -c/a
And here comes the trick: Add (b/2a)^2 to both sides of the equation
x^2 + b/a x + (b/2a)^2 = -c/a + (b/2a)^2
Note by adding it to both sides the equation still holds.
The left side can now be factorized as follows, and we add the terms on the right
(x + b/2a)^2 = (-4ac b^2)/4a^2
You can see the formula taking shape. We square root both sides
x + b/2a = +/- SQRT( (-4ac b^2)/4a^2) )
we simplify the left and bring the terms from the right over
x = -b/2a +/- SQRT( b^2 - 4ac )/2a
x= (-b/2a +/- SQRT( b^2 -4ac )) / 2a
And there is the formula
Note that this method can be used to solve a quadratic equation and is known as completing the square.
Answer:
Yes you can
Step-by-step explanation:
Take the general quadratic function:
F(x) = ax^2 + bx + c
Now lets set F(x) to 0
ax^2 + bx + c = 0
And we move c across
ax^2 + bx = - c
and we divide throughout by a
x^2 + b/a x = -c/a
And here comes the trick: Add (b/2a)^2 to both sides of the equation
x^2 + b/a x + (b/2a)^2 = -c/a + (b/2a)^2
Note by adding it to both sides the equation still holds.
The left side can now be factorized as follows, and we add the terms on the right
(x + b/2a)^2 = (-4ac b^2)/4a^2
You can see the formula taking shape. We square root both sides
x + b/2a = +/- SQRT( (-4ac b^2)/4a^2) )
we simplify the left and bring the terms from the right over
x = -b/2a +/- SQRT( b^2 - 4ac )/2a
x= (-b/2a +/- SQRT( b^2 -4ac )) / 2a
And there is the formula
Note that this method can be used to solve a quadratic equation and is known as completing the square.