Question

Solve the following quadratic equation:

`2/x^2 - 5/x + 2 = 0`

Answer 1

Given:

`2/x^2 - 5/x + 2 = 0` 

⇒ 2 – 5x + 2x² = 0   ...[Multiplying both sides by x²]  

⇒ 2x² – 5x + 2 = 0 

⇒ 2x² – (4x + x) + 2 = 0 

⇒ 2x² – 4x – x + 2 = 0 

⇒ 2x(x – 2) – 1(x – 2) = 0 

⇒ (2x – 1) (x – 2) = 0 

⇒ 2x – 1 = 0 or x – 2 = 0 

⇒ x = `1/2` or x = 2 

Hence, the roots of the equation are `1/2` and 2.