What are the solutions to the equation ax^2-x(2a^2+1)+2a=0 ?

The solutions to the equation ax^2-x(2a^2+1)+2a=0 are x=2a,x= 1/a ;\quad a\ne 0

Find the zeros of ax^2-x(2a^2+1)+2a=0

The zeros of ax^2-x(2a^2+1)+2a=0 are x=2a,x= 1/a ;\quad a\ne 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x = 2 a, x = \frac{1}{a}; a \neq = 0

Solution steps

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

Write in the standard form

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

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

Solve with the quadratic formula

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

Simplify

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

x_{1, 2} = \frac{- ( - 2 a ^{2} - 1 ) \pm ( 2 a + 1 ) ( 2 a - 1 )}{2 a}; a \neq = 0

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 2 a, x = \frac{1}{a}; a \neq = 0

35 x^{2} + 2835 x = 0

2 x^{2} + 5 = - 45

x^{2} + 128 = 0

(x + 1) (x + 2) = 30

\frac{x ^{2}}{4} + 9 = 0

What are the solutions to the equation ax^2-x(2a^2+1)+2a=0 ?
The solutions to the equation ax^2-x(2a^2+1)+2a=0 are x=2a,x= 1/a ;\quad a\ne 0
Find the zeros of ax^2-x(2a^2+1)+2a=0
The zeros of ax^2-x(2a^2+1)+2a=0 are x=2a,x= 1/a ;\quad a\ne 0