Ecuatia de gradul 2 Lesson Slides: 6 Slides (Grade 8)

6 Slides • 2 Questions

1

Ecuatia de gradul 2

2

O ecuatie de forma $ax^2+bx+c=0\ ;a,b,c∈R\ (a≠0)$
se numeste ecuatie de gradul 2

3

Pentru rezolvarea ecuatie se calculeaza intai discriminantul (delta):

$∆=b^2-4ac$

4

In functie de delta intalnim 3 cazuri:

$Daca\ \Delta>0;$ ecuatia are 2 solutii reale distincte: $x_1=\frac{-b+\sqrt{\Delta}}{2}$ si $x_2=\frac{-b-\sqrt{\Delta}}{2}$
$Daca\ \Delta=0;\$ ecuatia are o singura solutie: $x=\frac{-b}{2a}$
$Daca\ \Delta<0;\$ ecuuatia nu are solutii reale

5

Exemplu: $x^2+8x+12=0$

a = 1
b = 8
c = 12
$∆=8^2-4∙1∙12=64-48=16>0$
$x_1=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-8+4}{2\cdot1}=\frac{-4}{2}=-2$
$x_2=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-8-4}{2\cdot1}=\frac{-12}{2}=-6$

6

Fill in the Blanks

Se da ecuatia: $x^2-5x\ +6=0$

\Delta

=

Type answer...

7

Tema: sa se rezolve urmatoarele ecuatii:

$x^2+2x+1=0$
$x^2+x+1=0$
$3x^2-2x-8=0$

8

Multiple Select

Solutiile ecuatiei $x^2-5x\ +6=0$ sunt

1

-2

2

3

4

-3

Ecuatia de gradul 2

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