How many real solutions does x2+6x+13=0 have?

Question

asked Jun 23, 2021 58.6k views

1 Answer

Philip JF · Answer 1 · 2021-06-28T19:50:34+0000

Answer:

There are NO real solutions to this equation as per the study of its discriminant.

Explanation:

In order to answer the question, one needs to examine the "discriminant" associated with this quadratic equation.

Recall that the discriminant of a quadratic equation of the form:

$a\,x^2+b\,x+c=0$

is given by:
$b^2-4\, (a)\,(c)$

in our case :
$a=1\, ,\,b=6\,, and\,\,\,c=13$

Then the discriminant becomes:

$b^2-4\, (a)\,(c)=6^2-4\,(1)\,(13) =36-52=-16$

The discriminant is then a negative number, which means that there are NO real solutions (its solutions must involve imaginary numbers)