Question

derive quadratic formula​

Answer 1

Answer:

ax²+bx+c=0

x²+(b/a)x+c/a = 0

x² +2×(b/2a)x +c/a= 0

x² +2×(b/2a)x + (b/2a)² - (b/2a)² + c/a= 0

(x+(b/2a))² - b²/4a² +c/a = 0

(x+(b/2a))² = b²/4a² -c/a

(x+(b/2a))² = (b²-4ac)/4a²

take square root,

x + (b/2a) = ±√(b²-4ac)/2a

x = -(b/2a)±√(b²-4ac)/2a

Hence, proved!

Step-by-step explanation:

Answer 2

1) Divide both sides of the equation ax2 + bx + c = 0 by a.

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

3) Complete the square by adding b2 / 4a2 to both sides of the equation.

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