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1. 填空题.
(1)已知$x_{1},x_{2}是一元二次方程x^{2}-2x - 1 = 0$的两根,则$\frac{1}{x_{1}}+\frac{1}{x_{2}}=$
(2)已知一元二次方程$x^{2}+3x - 4 = 0的两根为x_{1},x_{2}$,则$x_{1}^{2}+x_{1}x_{2}+x_{2}^{2}=$
(3)已知关于$x的一元二次方程mx^{2}-4x - 6 = 0的两根为x_{1}和x_{2}$,且$x_{1}+x_{2}= -2$,则$m=$
(4)已知$x_{1},x_{2}是方程2x^{2}+3x - 4 = 0$的两个根,那么$x_{1}+x_{2}=$
(1)已知$x_{1},x_{2}是一元二次方程x^{2}-2x - 1 = 0$的两根,则$\frac{1}{x_{1}}+\frac{1}{x_{2}}=$
-2
.(2)已知一元二次方程$x^{2}+3x - 4 = 0的两根为x_{1},x_{2}$,则$x_{1}^{2}+x_{1}x_{2}+x_{2}^{2}=$
13
.(3)已知关于$x的一元二次方程mx^{2}-4x - 6 = 0的两根为x_{1}和x_{2}$,且$x_{1}+x_{2}= -2$,则$m=$
-2
,$x_{1}\cdot x_{2}=$3
.(4)已知$x_{1},x_{2}是方程2x^{2}+3x - 4 = 0$的两个根,那么$x_{1}+x_{2}=$
$-\frac{3}{2}$
,$x_{1}\cdot x_{2}=$-2
,$x_{1}^{2}+x_{2}^{2}=$$\frac{25}{4}$
,$(x_{1}+1)(x_{2}+1)=$$-\frac{5}{2}$
.答案
(1)-2
(2)13
(3)-2,3
(4)$-\frac{3}{2},-2,\frac{25}{4},-\frac{5}{2}$
2. 不解方程,求下列各方程的两根之和与两根之积.
(1)$x^{2}+3x + 1 = 0$.
(2)$3x^{2}-2x - 1 = 0$.
(3)$-2x^{2}+3 = 0$.
(4)$2x^{2}+5x = 3$.
(1)$x^{2}+3x + 1 = 0$.
(2)$3x^{2}-2x - 1 = 0$.
(3)$-2x^{2}+3 = 0$.
(4)$2x^{2}+5x = 3$.
答案
(1)$x_{1}+x_{2}=-3,x_{1}x_{2}=1$
(2)$x_{1}+x_{2}=\frac{2}{3},x_{1}x_{2}=-\frac{1}{3}$
(3)$x_{1}+x_{2}=0,x_{1}x_{2}=-\frac{3}{2}$
(4)$x_{1}+x_{2}=-\frac{5}{2},x_{1}x_{2}=-\frac{3}{2}$
