وحدة الجبر العاشر
- 2. 2
a 0 , ax bx c 0
2
b b 4ac
x
2a
x 2 a
x b
c
- 3. 2
x 10x 16 0
a 1 , b 10 , c 16
b b2 4ac
x
2a
10 (10)2 4(1)(16) 10 6
x
2(1) 2
10 6 4 10 6 16
x 2 x 8
2 2 2 2
- 4. 2
2x 4x 7
2
2x 4x 7 0
a 2 , b 4 , c 7
b b 2 4ac
x
2a
4 (4) 2 4(2)( 7) 4 72
x
2(2) 4
x 3.12 x 1.12
- 8. 2
4x 4x 1 0
a 4 , b 4 , c 1
2 2
b 4ac (4) 4(4)(1) 0
0
- 9. 2x 2 2x 3 0
a 2 , b 2 , c 3
2
b 4ac (2) 2
4(2)( 3) 28
- 10. 2
x 4x 6 0
a 1 , b 4 , c 6
2
b 4ac ( 4) 2 4(1)(6) 8
- 11. 4x 2 bx 1 0 b
2
b 4ac 0
2
b 4(4)( 1) 0
2
b 16
b 16 4
- 12. 2
3x 8x c 0 c
2
b 4ac 0
- 13. m , n ax 2 bx c 0
b
m n
a
c
m n
a
2 2 2
m n (m n ) 2mn
1 1 m n b
m n mn c
- 14. 4x 2 8x 3
2
4x 8x 3 0
a 4 , b 8 , c 3
b 8
1) m n
4
2
a
c 3
2) mn
a 4
2 2 2 3 5
3) m n (m n ) 2mn (2) 2
2( )
4 2
1 1 m n b 8
4)
m n mn c 3
- 15. 3x 2 2x 3 0
a , b , c
1) m n
2) mn
2 2
3) m n
1 1
4)
m n
- 16. 2x 2 bx 5 0
b
b
m n
a
b
1
2
b 2
- 17. b
5 2
3
bx 5x 3 0
b
m n
a
- 18. a 0 , ax 2 bx c 0
m , n
2
x (m n )x mn 0
5 , 3
x 2 (m n )x mn 0
x 2 (5 3)x (5 3) 0
2
x 8x 15 0
- 19. 2
3 ,
3
2
x (m n )x mn 0
2 2 2
x (3 )x (3 ) 0
3 3
2 11
x x 2 0
3
- 20. 2 3 , 3
2
x (m n )x mn 0
2
x (2 3 3)x (2 3 3) 0
2
x 3x 6 0
- 21. -5
2
x (m n )x mn 0
2
x ( 5) x (6) 0
2
x 5x 6 0