Question about quadratic equation and absolute value (combined one) problem is in comments

Question

zyberg · Answer

$$x^{2} + 5 |x| + 4 = 0$$

zyberg · Answer

My book says that there are no solutions, however, I don't understand why?

zyberg · Answer

The solutions that I worked out were x = -1 or -4. Why is that wrong?

welshfella · Answer

the |x|  must be positive    so -1 and -4  are not solutions

try  plugging in -1 and -4  and you see you cant get 0

zyberg · Answer

Ohh! That got me! Thank you very much! Are there any possible ways to indicate, if an equation with absolute value won't have any roots? @welshfella

welshfella · Answer

Not sure. But a quadratic of the form x^2 +b|x| + c = 0   where  b and c are positive will have no solution.

zyberg · Answer

Okay, thank you again @welshfella ! :)

welshfella · Answer

yw