SOLUTION: "The equation x^2-3x+k^2=4 has two distinct real roots. Find the possible values of k." I've already tried plugging in small integers such as ±1 and ±2 which has yielded answers bu

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: "The equation x^2-3x+k^2=4 has two distinct real roots. Find the possible values of k." I've already tried plugging in small integers such as ±1 and ±2 which has yielded answers bu      Log On


   

Question 978529: "The equation x^2-3x+k^2=4 has two distinct real roots. Find the possible values of k." I've already tried plugging in small integers such as ±1 and ±2 which has yielded answers but I want to know how to properly approach the problem and obtain all the possible solutions. Thanks.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Completely general-form quadratic equation:
x%5E2-3x%2Bk%5E2-4=0

Use the discriminant for finding the answer to the question. You want a discriminant that is POSITIVE.

Discriminant, %28-3%29%5E2-4%2A1%2A%28k%5E2-4%29%3E0.
Simplify,9-4%28k%5E2-4%29%3E0
9-4k%5E2%2B16%3E0
-9%2B4k%5E2-16%3C0
4k%5E2%3C25
k%5E2%3C25%2F4----Last good step before mistake.
cross%28k%3C5%2F4%29,k%3C5%2F2, bu a more complete and correct solution here is cross%28-5%2F4%3Ck%3C5%2F4%29highlight%28-5%2F2%3Ck%3C5%2F2%29.

Your trial of k=-1 or k=1 will work.
Your trial of k=-2 or k=2 will also work.


--
simply staying with k%3C5%2F2 is not adequate. It would include too many incorrect values.