Linear Equation can have degree of at most 1 and has only one solution. Quadratic Equation can have degree of at most 2 and has two solutions.
General form of quadratic equation: ax2 + bx + c = 0, where a, b and c are constants. Note that maximum degree of x is 2.
Unlike linear equations, any quadratic equation always has two solutions called roots of quadratic equation. After solving quadratic equation, you will get two values of x. To solve quadratic equation, you can use directly quadratic formula.
x = [-b ± √(b2-4ac)]/2a
In the above quadratic formula, the expression underneath the square root sign is called the discriminant of the quadratic equation. Discriminant is used to find the nature of roots.
Δ = b2 - 4ac
Case 1: Δ > 0
Real and distinct roots
Case 2: Δ = 0
Real and one distinct root (two same roots)
Case 3: Δ < 0
Roots are imaginary and occur as complex conjugates of each other
Let α and β be the roots of quadratic equation x2 + px + q = 0
x2 + px + q = (x-α)(x-β)
x2 + px + q = x2 - (α+β)x + αβ
q = αβ
Sum of the roots} = -p
Product of roots} = q