Thread: Quadratic equation question (with absolute function)

If "a" is strictly negative and is not equal to -2 thenthe equation

x^2 + a |x| + 1 = 0

a. cannot have any real roots
b. must have exactly four real roots or zero real roots
3. must have exactly 2 real roots
4. must have 2 or 4 real roots

please help me out on how to solve this question.

thanks

Originally Posted by champrock

If "a" is strictly negative and is not equal to -2 thenthe equation

x^2 + a |x| + 1 = 0

a. cannot have any real roots
b. must have exactly four real roots or zero real roots
3. must have exactly 2 real roots
4. must have 2 or 4 real roots

please help me out on how to solve this question.

thanks

Hi

If x > 0 the equation is x² + a x + 1 = 0
If x < 0 the equation is x² - a x + 1 = 0

In both cases if -2 < a < 0 there are no roots because the discriminant is < 0

If a < -2 then the discriminant is > 0, you can show that there are 2 real roots which are both > 0 (in the case where x > 0) or both < 0 (in the case where x < 0). There are therefore 4 real roots.

The answer is b