Sandi C.

asked • 12/26/16

find all values of h 9x^2-3x+3h=0

h=   ? 

Sandi C.

I'm working on discriminant of a quadratic equation with parameter.  I get to h=-1/12 but am not all together sure about the equals too.
Report

12/26/16

Michael J.

If you had given the full details of your question intiatially, then I could have provided you a better answer than the one I had given.
Report

12/26/16

Michael J.

This was a poorly written question to begin with.
Report

12/26/16

2 Answers By Expert Tutors

By:

Mark M. answered • 12/26/16

Tutor
4.9 (954)

Math Tutor--High School/College levels
About this tutor ›
About this tutor ›
9x2-3x+3h = 0
 
divide both sides by 3 to get 3x2-x+h = 0
 
x = [1 ± √(1-12h)]/6
 
If 1-12h = 0 (h = 1/12), the equation has 2 equal real roots.
 
If 1-12h > 0 (h < 1/12), the equation has two distinct real roots.
 
If 1-12h < 0 (h > 1/12), the equation has two imaginary roots that are                                        conjugates of each other.
 
Upvote • 2 Downvote
More
Report

Kenneth S.

Mark's answer is the BEST.  Once simplified by division by common factor 3, you can calculate the discriminant, which is 1 - 4(3)h) and, when discriminant is zero, there is ONE Real "double" root.
When discriminant is positive, there are two Real roots.
When discriminant is negative, there are two Imaginary roots (a conjugate pair).
 
Michael J points out that the question is imperfect.
 
Sandi's "getting to h = -1/12" is erroneous (wrong sign), but suggests that the question might have had some condition on the nature of the roots omitted from her submission.
Report

12/26/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.