Question

Proof for quadratic formula

Answer 1

The quadratic equation in standard form is
ax²+bx+c=0 , a≠0
dividing each term of the equation by a, we get
x+b/x+c/a=0
shifting constant term of equation by a, we have
X2+b/a x=c/a
adding (b/2a)² on both sides, we obtain
x²+b/a x+(b/2a)²=(b/2a)4-c/a=b²/4a²-c/a
or (x+b/2a)²=(b²-4ac)÷4a²
taking square root of both sides
√(x+b/2a)²=±√(b²-4ac)÷4a²
or x+b/2a=±√(b²-4ac)÷2a=> x=-b/2a±√(b²-4ac)÷2a= {-b±√(b²-4ac)}÷2a
thus x={-b±√(b²-4ac)}÷2a , a≠0 is quadratic formula

Answer 2

hope you get the proof.......