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受欢迎的代数 >

(2a+1)x^2+(-5a-10)x+(3a-1)=0

解答

(2 a + 1) x^{2} + (- 5 a - 10) x + (3 a - 1) = 0

解答

x = \frac{5 a + 10 + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}, x = \frac{5 a + 10 - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}; a \neq = - \frac{1}{2}

求解步骤

(2 a + 1) x^{2} + (- 5 a - 10) x + (3 a - 1) = 0

展开

(2 a + 1) x^{2} + (- 5 a - 10) x + (3 a - 1) : 2 a x^{2} + x^{2} - 5 a x - 10 x + 3 a - 1

2 a x^{2} + x^{2} - 5 a x - 10 x + 3 a - 1 = 0

改写成标准形式

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

(2 a + 1) x^{2} - (5 a + 10) x + 3 a - 1 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 5 a - 10 ) \pm ( - 5 a - 10 ) ^{2} - 4 ( 2 a + 1 ) ( 3 a - 1 )}{2 ( 2 a + 1 )}

化简

(- 5 a - 10)^{2} - 4 (2 a + 1) (3 a - 1) : a^{2} + 96 a + 104

x_{1, 2} = \frac{- ( - 5 a - 10 ) \pm a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}; a \neq = - \frac{1}{2}

将解分隔开

x_{1} = \frac{- ( - 5 a - 10 ) + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}, x_{2} = \frac{- ( - 5 a - 10 ) - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}

x = \frac{- ( - 5 a - 10 ) + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )} : \frac{5 a + 10 + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}

x = \frac{- ( - 5 a - 10 ) - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )} : \frac{5 a + 10 - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}

二次方程组的解是:

x = \frac{5 a + 10 + a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}, x = \frac{5 a + 10 - a ^{2} + 96 a + 104}{2 ( 2 a + 1 )}; a \neq = - \frac{1}{2}

作图

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