Question

what is the quadratic equation?​

Answer 1

Answer:

a quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown, and a, b and c represent known numbers, where a ≠ 0.

Answer 2

Answer:

I hope it is helpful

Step-by-step explanation:

Definitions:

A quadratic equation is a second- order polynomial equation in a single variable x

a×2+bx+c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots x can be found by completing the square,

ax2+bx+c=0

x2+bax=−ca

(x+b2a2)=−ca+b24a2=b2−4ac4a2

x+b2a=±b2−4ac−−−−−−−√2a

Solving for x then gives

x=−b±b2−4ac−−−−−−−√2a

The expression

b²−4ac

that appears in the quadratic formula under the square root plays an important role in solving quadratic equations. Because of its importance:

b²−4ac

is called the determinant of the quadratic equation

ax²+bx+c=0

There are three possible cases:

b² - 4ac > 0. In this case, the equation has two distinct real roots.

b² - 4ac = 0. In this case, the equation has one real root. (called a double root).

b² - 4ac < 0. In this case, the equation does not have real roots.