Question

$\bold\red{Quadratic \: Equation: \: ax^2+bx+c=0}$​

Answer 1

Answer:

Quadratic equation is a second order polynomial with 3 coefficients - a, b, c.

The quadratic equation is given by:

ax2 + bx + c = 0

The solution to the quadratic equation is given by 2 numbers x1 and x2.

We can change the quadratic equation to the form of:

(x - x1)(x - x2) = 0

Quadratic Formula

The solution to the quadratic equation is given by the quadratic formula:

 



 

The expression inside the square root is called discriminant and is denoted by Δ:

Δ = b2 - 4ac

The quadratic formula with discriminant notation:



This expression is important because it can tell us about the solution:

When Δ>0, there are 2 real roots x1=(-b+√Δ)/(2a) and x2=(-b-√Δ)/(2a).

When Δ=0, there is one root x1=x2=-b/(2a).

When Δ<0, there are no real roots, there are 2 complex roots:

x1=(-b+i√-Δ)/(2a) and x2=(-b-i√-Δ)/(2a).