Ecuaciones de Segundo Grado. Matematicas 1

Fórmula  : x=  -b ± √ b ² - 4ac      

                                     2a

1)  7x² + 21x - 28 = 0

 ax² +bx +c = 0

a = 7

b = 21

c = -28

= - (21) ± √ (21) ²  - 4 · 7 (-28)

           2(7)

= - 21 ± √ 441 – (-784)

                14

= -21± √ 1225

            14

= - 21 ± 35

           14

= -21 + 35 = 1

            14

= - 21 – 35 = - 4

             14

X₁ = 1

X₂ = -4

2) − x² + 6x − 9 = 0.

ax² +bx +c = 0

a = −1  

b = 6

c = −9

= -6 ± √ 6² – 4 (-1) (-9)

                 2(-1)

= -6 ± √ 36 – 36

          -2

= -6 ± √ 0

       -2

-6  =  3

-2

3) 2x² – 7x + 3 = 0

ax² +bx +c = 0

a = 2

b = 7

c = 3

= 7 ± √ 7² – 4 ·2·3

               4

= 7 ± √ 49 – 24

            4

= 7 ± √ 25

        4

= 7 ± 5

       4

= 12 = 3

    4

2 = 1

4    2

x₁ = 3

x₂ = 1/2

4) x² – 7x + 10 = 0

ax² +bx +c = 0

a = 1

b = 7

c = 10

= 7 ± √ 7² – 4 · 10

                2

= 7 ± √ 49 – 40

           2

= 7 ± √ 9

       2

= 7 ± 3

      2

= 10  = 5

    2

= 4 = 2

  2

x₁ = 5

x₂ = 2

5) x ² - x = 0

ax² +bx +c = 0

a = 1

b = - 1

c = 0

x=  -b ± √ b ² - 4ac      

              2ª

= - (-1) ± √ (-1) ² – 4· 1· 0

                        2·1

= 1 ± √ 1 – 0

            2

= 1 ± √ 1

          2

= 1 ± 1

         2

= 1+1  = 1

     2

= 1-1 = 0

     2

X₁ = 1

X₂ = 0