4a2x2+ 4abx+ 4ac=0;
(2ax+b)2-(b2-4ac)=0;
(2ax+b)2-()2=0.
.
.
22--3=0;
=2; b=1; c=-3;
D=(-1)2-4 2(-3)=25;
x1= = = ;
x2= =- =-1.
:
1) D 0;
2) D=0;
3) D 0.
ax2+bx+c=0 , :
1. ;
2. , ;
3. , , .
D | a | b | c | x1 | x2 | |
+ | + | - | + | + | + | |
+ | + | + | + | - | - | |
+ | + | + | - | - | + | |
+ | + | - | - | - | + | |
+ | - | + | + | + | x1=x2 | |
+ | + | + | - | - | x1=x2 | |
- | + | + | + | ij . | ||
- | + | - | + |
x2+ x+ =0
1. 0, 12 0, 1 2 :
) - 0, 1 + 2 0 1 0 2 0;
) - 0, 1 + 2 0 1 0 2 0;
2. 0, 1 0, 1 2 - :
) - 0, 1 + 2 0, ;
) - 0, 1 + 2 0 ;
3. b=0, 0, = .
:
1. , ,
ax2+bx+c=0; x1: x2
cx2+bx+a=0;
c + +a=c ax2+bx+c=0.
2. ax2+bx+c=0 b, , ;
3. , ;
4. 0 D=0, ;
5. a+b+c=0, 1=1, 2= ;
6. a-b+c=0, 1=-1, 2=- .
³ ( ). ³ . . , ³. , , , , .
ϳ ³ :
1. ;
2. ;
3. ;
4. .
:
1) ax2+bx+c:
) ;
) ;
) , , b;
) ;
2) x2+px+q, q=m2h, p=md:
) m m2, p q m m2;
) l p q m m2;
) , l, ;
|
|
) m.
³ (). , 1+2=-
12= .
³ (). m n , , q, x2+px+q=0.
. m+n=-p
mn=q;
x2-(m+n)x+mn=0;
x2-mx=nx+mx=0 x(x-m)n(x-m)=0 (x-m)(x-n)=0.
1,2 x2+px+q Sn=x1n+x2n, (n 2, nN),
Sn+1=-pSn-qSn-1, S1=-p, S2=p2-2q.
. 1,2 ,
12+px1+q=0/ 1n-1;
22+px2+q=0/ 2n-1;
x1n+1+px1n+qx1n-1=0
x2n+1+px2n+qx2n-1=0;
x1n+1+x2n+1+p(x1n+x2n)+q(x1n-1+x2n-1)=0.
.
.
22-5+1
1+2= ;
12= ;
13+23= ( - )= .