III. PHAN PHOI TH 6I LUONG
3. He bat phuong trinh bae ha
H2. Hay giai bat phuang trinh thii 2 trong he.
H3. Hay bieu dien cac tap nghiem tren, tren ciing mdt mat phing toa do. H4. Hay lay giao hai tap nghiem va neu tap nghiem cua he.
• Thuc hien H3
Hoat ddng cua GV Cau hdi 1.
Tim tap nghiem ciia bat phuang trinh:
2x + l > 5 .
Cau hdi 2.
Hay tim tap nghiem cua bat phuang trinh :
2 x ^ - 9 x + 7 > 0
Cau hdi 3.
Hay bieu dien hai tap nghiem tren, tren true so va neu tap nghiem ciia he.
Hoat ddng ciia HS Ggi y tra Idi cau hdi 1
S = ( 2 ; OD).
Ggi y tra Idi cau hdi 2
T = ( - c » ; 1 ] L J [ | ; + cx))
Ggi y tra Idi cau hdi 3
GV tu lam.
• GV neu vi du 5 va hudng din H thuc hien theo cac cau hdi sau day. HI. Vdi m = 2, phuong trinh da cho cd nghiem hay khdng?
H2. Vdi m 7^ 2, vdi dieu kien nao thi bat phuang trinh cd nghiem. H3. H3. Tim m de ba't phuong trinh cd nghiem.
MOT SO CAU HOI T R A C NGHIEM
1. Giai bat phuong trinh x^ - 3x + 3 < 0 cd nghiem la
( a ) x < l ; ( b ) x > 3 ;
(c) 1 < X < 3; (d) X G M. 126
Hay chgn ke't qua diing.
Trd lai. Chgn (c).
2. Cho ba't phuang trinh x^ - 2 73 x + 1 > 0 cd tap nghiem la S.
(a) 1 G S; (b) - 1 G S;
(c) 5 G S; (d) - . s.
Hay chgn ket qua diing.
Trd Idi. Chgn (c).
3. Cho bat phuong trinh 2x + 1 > 0 cd tap nghiem S va bit phuang trinh x - 2 73 x + 1 > 0 cd tap nghiem K Khidd
(a) K c S; (b) S c K;
(c) S n K = 0 ; (d) ca ba cau tren deu sai. Hay chgn ket qua diing.
Trd Idi. Chgn (b).
4. Cho tam thiic f(x) = 73 x^ - 273 x + 1 Hay dien cac dau (+); (-) vao cac d trd'ng sau
X f(x) f(x) —oo 73-^3-73 (a) 73+^3-73 (b) -|-CxD (c)
Trd Idi. Lin lugt dien cac dau: + - - , +
5. Phuang trinh x + 2mx + m - 1 = 0 (a) cd nghiem Vm > 0;
(c) cd nghiem Vm ;
(b) cd nghiem Vm < 0; (d) ca ba cau tren deu sai.
Hay chgn ket qua sai.
Trd Idi. Chgn (c).
6. Cho bat phuong trinh (m - l)x^ + (3m - l)x + 3m - 5 = 0 (1) (a) (1) vd nghiem Vm; (b) (1) cd nghiem Vm; (c) (1) cd nghiem khi m = 1; (d) m ^t 1 he cd nghiem. Hay chgn ket qua diing.
Trd lai. Chgn (b).
7. f(x) = x^ - 2x + m - 3 > 0 Vx khi
(a) m < 1; (b) m < 2; (c) m > 4; (d) m > 3. Hay chgn ke't qua diing.
Trd Idi. Chgn (b).
8. Bat phuang trinh nao sau day cd tap nghiem chiia doan [0 ; 2]
( a ) x ^ - 2 > 0 ; ( b ) x 2 - 2 < 0 . ( c ) x ^ + l > 0 ; ( d ) x ^ + l < 0 Hay chgn ket qua diing.
Trd Idi. Chgn (c).
9. Bat phuang trinh nao sau day cd tap nghiem chiia doan [0 ; + oo)
( a ) x ^ - 2 > 0 ; ( b ) x ^ - 2 < 0 ( c ) x ^ + l > 0 ; ( d ) x ^ + l < 0 Hay chgn ke't qui diing.
Trd Idi. Chgn (c).
10. Bat phuang trinh nao sau day vd nghiem?
( a ) x ^ - 2 > 0 ; ( b ) x 2 - 2 < 0 .
(c) x^ + 1 > 0 ; (d) x^ + 1 < 0 Hay chgn ket qua dung.
Trd lai. Chgn (d).
11. Bit phuang trinh nao sau day cd tap nghiem chua tap nghiem cua bit phuong trinh:
x^ - 4x + 3 < 0.
.2
(a)x - 2 x + l > 0 ; ( b ) x 2 - 3 x + 2 < 0 ( c ) x 2 - 8 x - 9 < 0 : (d) A-2+3<0 Hay chgn ket qua dung.
Trd Idi. Chgn (c).
12. Bat phuang trinh nao sau day cd tap nghiem chiia tap nghiem cua bat phuong trinh:
x ^ - 4 x + 3 > 0 .
( a ) x ^ - 4 x + 4 > 0 ; ( b ) x 2 - 3 x + 2 < 0
(c) x 2 - 8 x - 9 < 0 ; ( d ) x 2 + 3 > 0 Hay chgn ket qua diing.
Trd lai. Chgn (d).
13. Bit phuang trinh x - 4x + m < 0 vd nghiem khi (a) m < 1 (b) m > 3 (c) m >2 (d) m < 2. Hay chgn ke't qua diing.
Trd Idi. Chgn (c).
14. Bat phuang trinh x - 4x + m < 0 cd nghiem khi (a) m < 1 (b) m > 3
Hay chgn ket qua diing.
Trd Idi. Chgn (d).
15. He bat phuang trinh
cd nghiem khi (a) m < - 3 ; (c) m > 2
Hay chgn ket qua diing.
Trd Idi. Chgn (a).
16. He bat phuong trinh
(a) Vd nghiem;
(c) Cd nghiem la mdt khoang; Hay chgn ket qua diing.
Trd Idi. Chgn (a).
HUdNG DAN B A I TAP SGK
Bail Hudng ddn cdu a) x - l > 0 x^ + 2x + m < 0 (b) m > - 3 ; (d) khdng cd m nao. x - l > 0 x^+2x + 4 < 0 (b) Cd nghiem la mdt doan; (d) Cd nghiem la hgp cac khoang.
Hoat ddng cua GV Cau hdi 1.
Hay xac dinh he so a va tinh A'.
Cau hdi 2.
Giai bat phuang trinh tren.
Hoat ddng ciia HS Ggi y tra Idi cau hdi 1
a = - 5 < 0.
A = 64 > 0.
Ggi y tra Idi cau hdi 2
T - 0 0
' 5 u (2 ; + CO).
Tra Idi cac cau con lai. b)T = 0 . e)T = R. d ) T = [ - 2 ; 3 ] . Bai 54. Huang ddn cdu b) Hoat ddng cua GV Cau hdi 1.
Hay dua bat phuang trinh vd dang < 0 .
• Qix)
Cau hdi 2.
Lap bang xet dau va giai bat phuang trinh tren.
Hoat ddng ciia HS Ggi y tra Idi cau hdi 1 Bat phuang trinh cd dang:
- x 2 + 4 x - 3 ^ Q x ^ - 3 x - 1 0
Ggi y tra Idi cau hdi 2
S = (-00 ; - 2 ] LJ [1 ; 3] u [5 ; + oc).
Tra Idi cac cau con lai
a)S = ( 0 ; l ) u ( 2 ; 4 ) u ( 7 ; + co).
c)S = [-6; - ^ ] u [ 5 ; + oo).
d)S = [-73 ; 73].
Bai 55.
De gidi bdi tap ndy HS edn:
Hudng ddn
HI. Hay chia cac trudng hgp ciia m de bieu thirc la tam thuc bae hai va nhi thuc bae nhat.
H2. Tinh A trong trudng hgp phuang trinh da cho la phuang trinh bae hai. H3. Tim m de phuang trinh cd nghiem.
b ) / ( x ) = ( 3 x 2 - 4 . v ) ( 2 x 2 - x - l ) ;
Ldm tuang tu cdu a)
Bai 56.
De gidi he bdt phuang trinh, HS edn tiidn thii theo cdc budc sau: - Gidi titng bdt phucmg trinh trong he.
- Bieu dien mdi tap nghiem ciia cdc bdt phuang trinh tren ciing mot he true tog do.
- Ldy giao cdc tap nghiem. Hudng ddn.
a)
H1. Hay giai bat phuang trinh 2x^ + 9x + 7 < 0 . H2. Hay giai bat phuang trinh x + x - 6 < 0.
H3. Bieu dien cac tap nghiem tren ciing mdt true toa do, lay giao va viet tap nghiem cua he.
Ddp sd. - 1 < X < 2 ;
b) Hudng ddn.
H1. Hay giai bat phuang trinh 4x^ - 5x - 6 < 0 . H2. Hay giai bat phuang trinh - 4 x ^ + 1 2 x - 5 < 0 .
H3. Bieu dien cac tap nghiem tren ciing mdt true toa do, lay giao va viet tap nghiem cua he.
Dap so. — < X < —;
4 2
c) Hudng ddn.
HI. Hay giai bat phuang trinh - 2 x ^ - 5 x + 4 < 0 132
H2. Hay giai bat phuong trinh - x ^ - 3x + 1 0 > 0 .
H3. Bieu dien cac tap nghiem tren cung mot true toa do, lay giao va viet tap nghiem cua he.
Dap so. -5 < X < hoac < x < 4 ;
4 4
d) Hudng ddn.
HI. Hay giai bat phuang trinh 2x^ + x - 6 > 0 H2. Hay giai bat phuong trinh 3x^ - 1 Ox + 3 > 0
H3. Bieu dien cac tap nghiem tren cung mdt true toa do, lay giao va viet tap nghiem cua he.