Question

2X^2-5x+2=0
Quadratic formula

Answer 1

The solutions are
`x_(1)=2\ and\ x_(2)=0.5`.

Explanation:

Given:

`2x^(2) -5x+2=0`

Now, to solve by using quadratic formula:

`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`

Here
`a=2,b=-5\ and\ c=2`

`x=\frac{-(-5)\pm \sqrt{(-5)^(2)-4* 2* 2}}{2* 2}`

Now, here we will take either
`x=(-(-5)+√(25-16))/(4)` and then
`x=(-(-5)-√(25-16))/(4)`.

`x=(-(-5)+√(25-16))/(4)`
`x=(-(-5)-√(25-16))/(4)`

`x=(5+√(9))/(4)`
`x=(5-√(9))/(4)`

`x=(5+3)/(4)`
`x=(5-3)/(4)`

`x=(8)/(4)`
`x=(2)/(4)`

`x_(1)=2`
`x_(2)=(1)/(2)=0.5`

Therefore, the solutions are
`x_(1)=2\ and\ x_(2)=0.5`.