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Quadratic Equations: Definition, Formula And Examples

Quadratic Equations: Definition, Formula And Examples

Quadratic Equations

Quadratic equations are one of the most important topics asked in various competitive exams such as Banking, SSC and others. Quadratic equations are generally simple to answer only if one follows a proper approach and formula. We are providing you with the Quadratic equations definition, formula and questions with answers to help you understand the concept in a better way. You can study from the notes provided below and get acquainted with the important tricks.

Quadratic Equations: Definition

Quadratic equations can be defined by the name “Quad” which means “Square” In a quadratic equation, one of the variables is squared. This type of equation is also called “Equation of degree 2”.

An algebraic expression of the form: ax² + bx + c = 0, where a ≠ 0, b, c ∈ R is called a quadratic equation.

The solutions of a quadratic equation can be found by equating to 0. The solutions are called ‘roots’ or ‘zeroes’.

Roots of the Quadratic Equations

A root of the quadratic equation ax² + bc + c = 0 is a number α (real or complex) such that a a²+ba+c=0 then (x-a) is factor of ax²+bx+c. The roots of the quadratic equation are

x=(-b±√(b²-4ac))/2a

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Quadratic Equations: Nature of Roots

The value of x at which value of the equation will be zero.

Roots are imaginary: b² – 4ac ≤ 0

Roots are real: b² – 4ac ≥ 0

Sum & product of roots 

Let there are two roots named α & β, then,

a=(-b+√(b²-4ac))/2a  & β=(-b-√(b²-4ac))/2a

Sum of root: α + β = (-b)/a

Product of root: αβ = c/a

Quadratic Equations: Examples