Question

solve the quadratic equation m^2-4m + 9 =0​

Answer 1

Answer:

Solving    m2-4m+9 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  m  , the solution for   Am2+Bm+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

           - B  ±  √ B2-4AC

 m =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -4

                     C   =   9

Accordingly,  B2  -  4AC   =

                    16 - 36 =

                    -20

Applying the quadratic formula :

              4 ± √ -20

  m  =    —————

                   2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)  

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -20  =  

                   √ 20 • (-1)  =

                   √ 20  • √ -1   =

                   ±  √ 20  • i