Question

Consider the quadratic equation x 2 = 4x - 5. How many solutions does the equation hase?

Answer 1

The equation has 2 non real solutions.

Explanation:

Given:

`x ^2 = 4x - 5`

To Find:

The solutions of the equation = ?

Solution:

Lets find the solution using the quadratic equation formula

`x ^2 = 4x - 5`

`x^2-4x +5 = 0`

`x = (-b \pm √(b^2-4ac))/(2a)`

Here

a = 1

b =-4

c = 5

Now Substituting the values,

`x = (-(-4) \pm √((-4)^2-4(1)(5)))/(2(1))`

`x = (4\pm √(16-20))/(2)`

`x = (4\pm √(-4))/(2)`

`x = (4\pm √(4)* √(-1))/(2)`

`x = (4\pm 2 √(-1))/(2)`

`x = (4\pm 2i)/(2)`

`x= (4+2i)/(2)`
`x= (4-2i)/(2)`

x= 2 + i x= 2-i