Question

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

Answer 1

\[x^{2} + 5 |x| + 4 = 0\]

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

Okay, thank you again @welshfella ! :)

Answer 8

yw