I Tavi

7 vietas Teorema
1 SeadgineT dayvanili kvadratuli gantoleba, Tu cnobilia,
rom misi fesvebia: x 1 =2, x 2 =3.
vietis Teorema:
Tu ax2 + bx + c = 0 kvadratuli gantolebis diskriminanti D≥0,
maSin misi fesvebis jami – b
­s, xolo fesvebis namravli
c
a
­s tolia .
a
damtkiceba:
rogorc cnobilia, roca D≥0 kvadratul gantolebas aqvs ori
amonaxseni (an gansxvavebuli an toli).
x 1 = , x 2 =
x + x = 1 2 +
− b +
=
2
b − 4ac − b −
2a
2
b − 4ac
=
= –2b b
= –
2a a .
xolo x ·x = 1 2 ·
2
2 2
( − b) + b − 4ac
= 2
4a
= c
a .
amrigad,
roca D≥0
x + x = – 1 2 b
a , x1 ·x c
= 2 a .
marTebulia vietis Teoremis Sebrunebuli Teoremac:
mocemuli x 1 da x 2 ricxvebi iseTi x 2 +px+q=0 gantolebis amonaxsnebia,
sadac p=–(x 1 +x 2 ) da q=x 1 x 2 .
magaliTi 1
amoxseniT gantoleba vietis Teoremis gamoyenebiT:
a) x 2 –x–12=0; b) x 2 +8x+15=0.
amoxsna:
a) –12 davSaloT mamravlebad:
–12=1·(–12)=(–1)·12=2·(–6)=(–2)·6=(–3)·4=3·(–4). vietis Teoremis Tanaxmad
miRebuli Tanamamravlebidan gantolebis amonaxsnebi
iqnebian isini, romelTa jamic 1-is tolia: –3+4=1.
e.i. x =–3, x =4.
1 2
fransua vieta
(1540-1603)
!Tu 2 x +bx+c=0, gantolebas
(a=1; b;c∉Z)
aqvs racionaluri
fesvebi, maSin
isini aucileblad
mTeli ricxvebia.
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