DH99 wrote:

If x is an integer, how many possible values of x exist for \(x^2+5|x|+6=0 ?\)

A. 4

B. 2

C. 3

D. 1

E. 0

Looking at other posts, I might be oversimplifying here . . . Please correct me if I'm mistaken.

One method: check the signs of the terms.

The squared term is positive (or nonnegative if x=0).

The term whose product is (+5) * (some nonnegative or positive number because absolute value nonnegative or positive), is positive or nonnegative (if x = 0).

The constant is positive.

You cannot sum three positive numbers, or two zeros (if x=0) and a positive, and get zero. No values will work.

Answer E Another way: If "check the signs method" doesn't occur to you, try factoring the quadratic as if there were no absolute value bars around the x in the second term.

\(x^2+5x+6=0\)

(x + 3)(x + 2)

So x = -3 or -2

Check the values. Plug -3 and -2 into original equation.

Neither works:

-3: 9 + 15 + 6 does not equal zero.

From the pattern of positive terms that result when plugging in a negative number (squared term is positive, absolute value term is positive, constant is positive), -2 will not work either.

From the

(+) +

(+) +

(+) pattern: you cannot get to 0 with three positive numbers. No values will work.

Answer E