Question

quadratic formula method



derivation ​

Answer 1

Answer:is actually derived using the steps involved in completing the square. It stems from the fact that any quadratic function or equation of the form y = a x 2 + b x + c y = a{x^2} + bx + c y=ax2+bx+c can be solved for its roots.

Step-by-step explanation:

Answer 2

$\large \pmb{ \bf{ \blue{Derivation \: of \: Quadratic \: Formula}}}$

ax² + bx + c = 0

$\tt \: x² + \frac {b}{a} x + \frac {c}{a} = 0 \\ \\ \tt \: x² + \frac{ b}{a} x = \frac{ −c}{a} \\ \\ \tt \: x²+ \frac {b}{a} x + \frac{b²}{4a²} = \frac {b²}{4a² }− \frac{c}{a } \\ \\ \tt \:{ \bigg(x+ \frac{b}{ 2 a} \bigg) }^{2} = \frac{ {b}^{2} - 4ac}{4a² }\\ \\ \tt x+ \frac{ b}{2a }= \frac{ ± \sqrt{b²−4ac}}{{2a}} \\ \\ \tt x = - \frac{ b}{2a } ± \frac{\sqrt{b²−4ac}}{{2a}} \\ \\ \large \boxed{\red { \bf \: x = \frac{ - b±\sqrt{ b²−4ac}}{{2a}}}}$