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人気のある代数 >

(a-1)x^2-(2a-3)x-2=0

解

(a - 1) x^{2} - (2 a - 3) x - 2 = 0

解

x = 2, x = - \frac{1}{a - 1}; a \neq = 1

解答ステップ

(a - 1) x^{2} - (2 a - 3) x - 2 = 0

拡張

(a - 1) x^{2} - (2 a - 3) x - 2 : a x^{2} - x^{2} - 2 a x + 3 x - 2

a x^{2} - x^{2} - 2 a x + 3 x - 2 = 0

標準的な形式で書く

a x^{2} + b x + c = 0

(a - 1) x^{2} + (- 2 a + 3) x - 2 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 2 a + 3 ) \pm ( - 2 a + 3 ) ^{2} - 4 ( a - 1 ) ( - 2 )}{2 ( a - 1 )}

簡素化

(- 2 a + 3)^{2} - 4 (a - 1) (- 2) : 2 a - 1

x_{1, 2} = \frac{- ( - 2 a + 3 ) \pm ( 2 a - 1 )}{2 ( a - 1 )}; a \neq = 1

解を分離する

x_{1} = \frac{- ( - 2 a + 3 ) + 2 a - 1}{2 ( a - 1 )}, x_{2} = \frac{- ( - 2 a + 3 ) - ( 2 a - 1 )}{2 ( a - 1 )}

x = \frac{- ( - 2 a + 3 ) + 2 a - 1}{2 ( a - 1 )} : 2

x = \frac{- ( - 2 a + 3 ) - ( 2 a - 1 )}{2 ( a - 1 )} : - \frac{1}{a - 1}

二次equationの解:

x = 2, x = - \frac{1}{a - 1}; a \neq = 1

グラフ

人気の例

x + x^{2} - 5 = 0

4 x^{2} - 101 x + 25 = 0

2 + 6 t - 4.9 t^{2} = 0

(s + 3) (s + 5) = 0

(5x+2)(5x-2)=(A+B)(A-B)

(5 x + 2) (5 x - 2) = (A + B) (A - B)