In elementary algebra, a quadratic equation is any equation having the form

ax^2+bx + c = 0

where x  represents an unknown, and a,\ b,\ and\ c  represent known numbers such that a is not equal to 0 .

If a = 0 , then the equation is linear, not quadratic.

The numbers a,\ b,\ and\ c  are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The degree of a quadratic equation is 2.

Examples of quadratic equations:m40x

21x^2-8x-4=0 \ where \ a=21, \ b=-8 \ and \ c=-4  

6x^2+5x-6=0 \ where \ a=6, \ b=5 \ and \ c=-6

Roots of Quadratic equations

Every quadratic equation ax^2+bx + c = 0  is satisfied by two values say p \  and \  q . These values, p \  and \  q , are said to be the root of the equation.

What this also means is that ax^2+bx + c  =  (x - p)(x - q) = 0

 

Solving Quadratic equations

There are two ways to solve the quadratic equations.

  1. Factorization Method
    • Step 1: Factorize ax^2+bx + c  =  (x - p)(x - q) = 0
    • Step 2: Equate each linear part to zero.
    • Step 3: Hence x = p \ and \ x = q

m41xUsing the formula

  • Step 1: From the quadratic equation, first identify a,\ b,\ and\ c .
  • Then use the following formula

x =\frac{-b\pm \sqrt{b^2-4ac}}{2a}

 

 

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