The document contains solutions to 33 quadratic equations. Each solution involves calculating the discriminant (Δ) of the equation by using the formula Δ = b2 - 4ac and finding the real roots using the quadratic formula. Real roots are written as solutions to the equations and equations without real roots are indicated as having no real roots.

1. Professora Andréia Santana
1) x² - 5x + 6 = 0
a=1
b= – 5
c=6
∆=
∆= (-5)² - 4.1.6
∆= 25 - 24
∆= 1
√∆ ( ) √
2) x² - 8x + 12 = 0
a=1
b= – 8
c=12
∆=
∆= (-8)² - 4.1.12
∆= 64 – 48
∆= 16
√∆ ( ) √

2. Professora Andréia Santana
3) x² + 2x - 8 = 0
a=1
b= 2
c=-8
∆=
∆= 2² - 4.1.(-8)
∆= 4+32
∆= 36
√∆ √
4) x² - 5x + 8 = 0
a=1
b= – 5
c=8
∆=
∆ ( )
∆ –
∆
Não possui raízes reais

3. Professora Andréia Santana
5) 2x² - 8x + 8 = 0
a=2
b= –8
c=8
∆=
∆= (-8)² - 4.2.8
∆= 64-64
∆= 0
√∆ ( ) √
6) x² - 4x - 5 = 0
a=1
b= – 4
c= – 5
∆=
∆= (-4)² - 4.1.(-5)
∆= 16 + 20
∆= 36
√∆ ( ) √

4. Professora Andréia Santana
7) - x² + x + 12 = 0
a= – 1
b= 1
c=12
∆=
∆= 1² - 4.(-1).12
∆= 1+48
∆= 49
√∆ √
( )
8) -x² + 6x - 5 = 0
a= – 1
b= 6
c= – 5
∆=
∆= ( ) ( )
∆= 36 – 20
∆= 16
√∆ √
( )

5. Professora Andréia Santana
9) 6x² + x - 1 = 0
a= 6
b= 1
c= – 1
∆=
∆= ( )
∆= 1+24
∆= 25
√∆ √
10) 3x² - 7x + 2 = 0
a= 6
b= 1
c= – 1
∆=
∆= ( )
∆= 1+24
∆= 25
√∆ √

6. Professora Andréia Santana
11) 2x² - 7x = 15  2x² – 7x – 15 = 0
a=2
b= -7
c= -15
∆=
∆= (-7)² - 4.2.(-15)
∆= 49 + 120
∆= 169
√∆ ( ) √
12) 4x² + 9 = 12x  4x² - 12x + 9 = 0
a=4
b= -12
c= 9
∆=
∆= (-12)² - 4.4.9
∆= 144 - 144
∆= 0
√∆ √

7. Professora Andréia Santana
13) x² = x + 12  x² - x – 12 = 0
a=1
b= 2
c=-8
∆=
∆= 2² - 4.1.(-8)
∆= 4+32
∆= 36
√∆ √
14) 2x² = -12x - 18  2x² +12x + 18 = 0
a=2
b= 12
c=18
∆=
∆= 12² - 4.2.18
∆= 144 - 144
∆= 0
√∆ √

8. Professora Andréia Santana
15) ( x - 5)² = 1
( )( )
a=1
b= -10
c= 24
∆=
∆= (-10)² - 4.1.24
∆= 100 - 96
∆= 4
√∆ ( ) √

9. Professora Andréia Santana
16) 25x² = 20x – 4
a=25
b= -20
c= 4
∆=
∆= (-20)² - 4.25.4
∆= 400 – 400
∆= 0
√∆ ( ) √
17) 2x = 15 – x²
a=1
b= 2
c= -15
∆=
∆= 2² - 4.1.(-15)
∆= 4+60
∆= 64
√∆ √

10. Professora Andréia Santana
18) x² + 3x – 6 = -8
a=1
b= 3
c= 2
∆=
∆= 3² - 4.1.2
∆= 9-8
∆= 1
√∆ √
19) x² + x – 7 = 5
a=1
b= 1
c= -12
∆=
∆= 1² - 4.1.(-12)
∆= 1+48
∆= 49
√∆ √

11. Professora Andréia Santana
20) 4x² - x + 1 = x + 3x²
a=1
b= -2
c= 1
∆=
∆= (-2)² - 4.1.1
∆= 4 - 4
∆= 0
√∆ ( ) √
21) 3x² + 5x = -x – 9 + 2x²
a=1
b= 6
c= 9
∆=
∆= 6² - 4.1.9
∆= 36-36
∆= 0
√∆ √

12. Professora Andréia Santana
22) 4 + x ( x - 4) = x
a=1
b= -5
c= 4
∆=
∆= (-5)² - 4.1.4
∆= 25 - 16
∆= 9
√∆ ( ) √
23) x ( x + 3) – 40 = 0
a=1
b= 3
c= -40
∆=
∆= 3² - 4.1.(-40)
∆= 9+160
∆= 169
√∆ √

13. Professora Andréia Santana
24) x² + 5x + 6 = 0
a=1
b= 5
c= 6
∆=
∆= 5² - 4.1.6
∆= 25-24
∆= 1
√∆ √
25) x² - 7x + 12 = 0
a=1
b= -7
c= 12
∆=
∆= (-7)² - 4.1.12
∆= 49-48
∆= 1
√∆ ( ) √

14. Professora Andréia Santana
26) x² + 5x + 4 = 0
a=1
b= 5
c= 4
∆=
∆= 5² - 4.1.4
∆= 25-16
∆= 9
√∆ √
27) ( 2x - 4)² = 0
( )( )
a=4
b= -16
c= 16
∆=
∆= (-16)² - 4.4.16
∆= 256-256
∆= 0
√∆ ( ) √

15. Professora Andréia Santana
28) x² - 18x + 45 = 0 _____(R:3,15)
a=1
b= -18
c= 45
∆=
∆= (-18)² - 4.1.45
∆= 324 - 180
∆= 144
√∆ ( ) √
29) -x² - x + 30 = 0
a=-1
b= -1
c= 30
∆=
∆= (-1)² - 4.(-1).30
∆= 1 + 120
∆= 121
√∆ ( ) √
( )

16. Professora Andréia Santana
30) x² - 6x + 9 = 0
a=1
b= -6
c= 9
∆=
∆= (-6)² - 4.1.9
∆= 36-36
∆= 0
√∆ ( ) √
31) ( x + 3)² = 1
( )( )
a=1
b= 6
c= 8
∆=
∆= 6² - 4.1.8
∆= 36-32
∆= 4
√∆ √

17. Professora Andréia Santana
32) x² + 3x - 28 = 0 (R: -7,4)
a=1
b= 3
c= -28
∆=
∆= 3² - 4.1.(-28)
∆= 9+112
∆= 121
√∆ √
33) x² - 3 = 4x + 2 (R: -1,5)
a=1
b= -4
c= -5
∆=
∆= (-4)² - 4.1.(-5)
∆= 16+20
∆= 36
√∆ ( ) √