Question

Consider the quadratic equation x squared = 4x - 5. how many solutions does the equation have?

Answer 1

Answer:

The quadratic equation has two complex solutions

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}=4x-5$  

Equate to cero

$x^{2}-4x+5=0$  

so

$a=1\\b=-4\\c=5$

substitute in the formula

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

$x=\frac{4(+/-)\sqrt{16-20}} {2}$

$x=\frac{4(+/-)\sqrt{-4}} {2}$

Remember that

$i^{2}=-1$

so

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

$x=2(+/-)i$

therefore

The quadratic equation has two complex solutions