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電子課本網(wǎng) 第6頁(yè)

第6頁(yè)

信息發(fā)布者:
$x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
公式法
沒(méi)有
C
D
$3x^{2}+7x - 2 = 0$
121
$m_1=-3,m_2=\frac{2}{3}$
$-5$
解:對(duì)于方程?$x^2-4x - 1 = 0,$?
其中?$a = 1,$??$b = -4,$??$c = -1。$?
?$ $?先計(jì)算判別式?$?=b^2-4ac$?
?$=(-4)^2-4×1×(-1)=16 + 4 = 20。$?
?$ $?再根據(jù)求根公式?$x=\frac {-b\pm \sqrt {b^2-4ac}}{2a}$?可得:
?$ x=\frac {4\pm \sqrt {20}}{2}=\frac {4\pm 2\sqrt {5}}{2}=2\pm \sqrt {5},$?
?$ $?所以?$x_{1} = 2+\sqrt {5},$??$x_{2} = 2-\sqrt {5}。$?
解:對(duì)于方程?$-3x^2+6x - 2 = 0,$?
其中?$a=-3,$??$b = 6,$??$c = -2。$?
?$ $?先計(jì)算判別式?$?=b^2-4ac=6^2-4×(-3)×(-2)$?
?$=36 - 24 = 12。$?
?$ $?再根據(jù)求根公式?$x=\frac {-b\pm \sqrt {b^2-4ac}}{2a}$?可得:
?$ x=\frac {-6\pm \sqrt {12}}{2×(-3)}=\frac {-6\pm 2\sqrt {3}}{-6}=\frac {3\pm \sqrt {3}}{3},$?
?$ $?所以?$x_{1}=\frac {3+\sqrt {3}}{3},$??$x_{2}=\frac {3-\sqrt {3}}{3}。$?
解:將方程?$2y^2-3 = 2y$?化為一般形式
?$2y^2-2y - 3 = 0,$?
其中?$a = 2,$??$b = -2,$??$c = -3。$?
?$ $?先計(jì)算判別式?$?=b^2-4ac$?
?$=(-2)^2-4×2×(-3)$?
?$=4 + 24 = 28。$?
?$ $?再根據(jù)求根公式?$y=\frac {-b\pm \sqrt {b^2-4ac}}{2a}$?可得:
?$ y=\frac {2\pm \sqrt {28}}{2×2}=\frac {2\pm 2\sqrt {7}}{4}=\frac {1\pm \sqrt {7}}{2},$?
?$ $?所以?$y_{1}=\frac {1+\sqrt {7}}{2},$??$y_{2}=\frac {1-\sqrt {7}}{2}。$?
解:將方程?$t^2+2\sqrt {3}t = 4$?化為一般形式
?$t^2+2\sqrt {3}t - 4 = 0,$?
其中?$a = 1,$??$b = 2\sqrt {3},$??$c = -4。$?
?$ $?先計(jì)算判別式?$?=b^2-4ac$?
?$=(2\sqrt {3})^2-4×1×(-4)$?
?$=12 + 16 $?
?$= 28。$?
?$ $?再根據(jù)求根公式?$t=\frac {-b\pm \sqrt {b^2-4ac}}{2a}$?可得:
?$ t=\frac {-2\sqrt {3}\pm \sqrt {28}}{2}=\frac {-2\sqrt {3}\pm 2\sqrt {7}}{2}=-\sqrt {3}\pm \sqrt {7},$?
?$ $?所以?$t_{1}=-\sqrt {3}+\sqrt {7},$??$t_{2}=-\sqrt {3}-\sqrt {7}。$?