SOLUTION: find the value of k so that the equation (3k^2)-(2x^2)+5x+3=0 has real and distinct roots.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: find the value of k so that the equation (3k^2)-(2x^2)+5x+3=0 has real and distinct roots.      Log On


   

Question 1009457: find the value of k so that the equation (3k^2)-(2x^2)+5x+3=0 has real and distinct roots.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%283k%5E2%29-%282x%5E2%29%2B5x%2B3=0 

Rearrange terms on the left side:

-2x%5E2%2B5x%2B3%2B3k%5E2=0

-2x%5E2%2B5x%2B%283%2B3k%5E2%29=0

Compare to

ax%5E2%2Bbx%2Bc=0

a=-2, b=5, c=3+3k²

The equation will have real and distinct roots if
the discriminant b²-4ac is positive.



Since 49%2B24k%5E2 will always be positive so for ALL real values
of k, the equation will always have real and distinct roots.

Edwin