How do you use the discriminant to determine the nature of the roots for $x^2 + 2x + 5 = 0$ ?

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Answer 1 · 2015-06-19T05:59:03

As $color(red)(Delta = -16$ (less than zero), this equation has two complex roots.

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

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:
$a=1, b=2, c=5$

The Discriminant is given by:
$Delta=b^2-4*a*c$
$= (2)^2-(4*(1)*5)$
$= 4-20=-16$

When, $Delta<0$ there are two complex solutions.
Here, $color(red)(Delta = -16)$ , so this equation has two complex roots

Note :
The solutions are normally found using the formula
$x=(-b+-sqrtDelta)/(2*a)$
Finding the solutions:
$x =( -2+-sqrt-16)/(2a$
$color(red)( x =( -2+4i)/2$ and $color(red)(x = (-2-4i)/2$

How do you use the discriminant to determine the nature of the roots for x^2 + 2x + 5 = 0x^2 + 2x + 5 = 0?