Question

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

Answer 1

Answer:

The equation has 2 non real solutions.

Step-by-step explanation:

Given:

$x ^2 = 4x - 5$

To Find:

The solutions of the equation = ?

Solution:

Lets find the solution using the quadratic equation formula

$x ^2 = 4x - 5$

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

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Here

a = 1

b =-4

c = 5

Now Substituting the values,

$x = \frac{-(-4) \pm \sqrt{(-4)^2-4(1)(5)}}{2(1)}$

$x = \frac{4\pm \sqrt{16-20}}{2}$

$x = \frac{4\pm \sqrt{-4}}{2}$

$x = \frac{4\pm \sqrt{4}\times \sqrt{-1}}{2}$

$x = \frac{4\pm 2 \sqrt{-1}}{2}$

$x = \frac{4\pm 2i}{2}$

$x= \frac{4+2i}{2}$                              $x= \frac{4-2i}{2}$

x= 2 + i                                  x= 2-i