Quadratic equation is a second degree polynomial equation; meaning of quadratic is “square”. Second degree polynomial equation has two solutions and these solutions may be real or complex. These solutions are called roots.
Ax2 + Bx + C = 0 this is a Quadratic Equation, where value of 'A' is not equals to zero.
In this equation 'x' is a variable and A, B, C are constant or quadratic equation, here in this equation. If value of A = 0, than this equation becomes a linear equation. Now we will come to next Point “how to solve quadratic sequences”.
Let ax2 + bx + c = 0 this is a basic quadratic equation. Roots are given by formula → (-b ∓ √(b2 – 4ac)) / 2a -----equation 1.
So in this case there are two solutions of this quadratic equation first one is with positive sign and second is with negative sign.
X1 = (-b + √(b2 - 4ac))/2a ----equation 2
X2 = (-b – √(b2 - 4ac)) /2a ----equation 3
Equation 2 and 3 both are the solutions of quadratic equation.
In equation 1, (b2 – 4ac) = D = discriminant.
So X1 = (-b + √(D)) / 2a and X2 = (-b - √(D)) /2a.
Case 1: If discriminant is positive then there are two roots and both are Real Numbers.
(-b + √(D)) / 2a , (-b – √(D)) / 2a.
Case 2: If discriminant is zero then there is only one distinct real root -b/2a.
Case 3: If discriminant is negative then there are two distinct complex (non real) roots
-b/2a + i √(-D)/2a and -b/2a – i √(D) / 2a.
Here 'i' is an imaginary unit.