Question 16705: find all values for k such that the equation 3x squared - 2x + k = 0 has imaginary roots
Answer by xcentaur(357)   (Show Source):
You can put this solution on YOUR website! 3x^2 - 2x + k = 0
For imaginary roots, discriminant(D) must be less than zero.
D=b^2-4ac is the discriminant.
D= (-2)^2 -4(3)(k)
= 4 - 12k
This must be less than zero.
Therefore, 4 - 12k < 0
4<12k
1<3k
1/3
Hence for all values of k which are less than 1/3,the roots will be imaginary.
For k=1/3,roots will be real and equal. All values of k greater than 1/3 will result in real distinct roots.
Hope this helps,
Prabhat
|
|
|
