SOLUTION: What should be the range of the value of k so that the equation 2x2+3kx-9=0 will have real and unequal roots? What should be the value of k so that the equation x2+(k-2)x+4=0 will

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: What should be the range of the value of k so that the equation 2x2+3kx-9=0 will have real and unequal roots? What should be the value of k so that the equation x2+(k-2)x+4=0 will      Log On


   

Question 549684: What should be the range of the value of k so that the equation 2x2+3kx-9=0 will have real and unequal roots?
What should be the value of k so that the equation x2+(k-2)x+4=0 will have equal roots?
Find the range of the value of k so that the equation kx2+4squareroot of 3x+k=0 will have imaginary roots.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant for 2x%5E2%2B3kx-9=0 is
%283k%29%5E2-4%2A2%2A%28-9%29=9k%5E2%2B72
The equation 2x%5E2%2B3kx-9=0 will have real and unequal roots when
9k%5E2%2B72%3E0 which happens for all real values of k.
The discriminant for x%5E2%2B%28k-2%29x%2B4=0 is
%28k-2%29%5E2-4%2A1%2A4=%28k-2%29%5E2-16
The equation x%5E2%2B%28k-2%29x%2B4=0 will have equal roots when
%28k-2%29%5E2-16=0 <--> %28k-2%29%5E2=16 which happens for k=6 and k=-2
Was the third equation kx%5E2%2B4sqrt%283%29x%2Bk=0?
The discriminant for kx%5E2%2B4sqrt%283%29x%2Bk=0 is
%284sqrt%283%29%29%5E2-4%2Ak%2Ak=48-4k%5E2=4%2812-k%5E2%29
The equation kx%5E2%2B4sqrt%283%29x%2Bk=0 will have imaginary roots when
12-k%5E2%3C0, which happens for abs%28k%29%3Esqrt%2812%29=2sqrt%283%29