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EQUATIONS -> Solution of a quadratic equation


  • Equations: common information

  • Main ways used at solving of equations

  • Linear equations

  • Quadratic equation

  • Solution of a quadratic equation

    Solution of a quadratic equation


    Formulas for solution of non-reduced
    brand reduced quadratic equation.

    In general case of a non-reduced quadratic equation:

    ax 2 + bx + c = 0 ,

     

    its roots are found by the formula:

    If to divide all terms of a non-reduced quadratic equation by  a (is it possible ?),  and to sign  b / a = p  and  c / a = q , then we’ll receive the reduced quadratic equation:

    x 2 + px + q = 0 ,

    roots of which are calculated by the formula:
                                                           


    E x a m p l e .   x 2 + 5x + 6 = 0 .  Here  p = 5,  q = 6. Then we have: 

                                                                                   

                                  

                            hence,   x1= – 5 / 2  + 1 / 2  = – 2 ,    x2 = – 5 / 2 – 1 / 2 = – 3

  • Properties of roots of a quadratic equation. Viete's theorem

  • Factoring of a quadratic trinomial

  • Equations of higher degrees




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