Question

Derive quadratic formula.

Answer 1

Hi,

The quadratic formula is x = - b+-root b^2 4ac
_____________
2a
i hope it helps

Answer 2

General form of Quadratic equation is
ax² + bx + c = 0

derivation of formulae for finding roots of Quadratic equation.
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ax² + bx + c = 0

ax² + bx = -c

divide both sides by a

x² + (b/a).x = -c/a

add both sides, ( b/2a)²

x² + 2.(b/2a).x + (b/2a)² = -c + (b/2a)²

[ use, formula , a² + 2ab + b² = (a + b)² ]

( x + b/2a)² = ( b² - 4ac)/4a²

take square root both sides,

(x + b/2a) = ± √(b² -4ac)/2a

x = -b/2a ± √(b² - 4ac)/2a

x = { - b ±√(b² - 4ac)}/2a