For the question:
Show that the equation (x^2 + 5x)/(7x + 9) = (1 - k)/(1 + k) has real roots for all values of k.
I know that for real roots, the discriminant has to be greater or equal than 0. I found out the discriminant, which is x^2 + kx^2 - 2x + 12 xk - 9k + 9 greater than or equal to 0. How do I make it into a quadratic equation?
Hmm I keep on getting 27k^2 - 12k + 10 as the discriminant but when I try to find k, there are no real solutions. What does that mean?
Good work, the discriminant is correct =)
Originally Posted by xwrathbringerx
Now, you want the discriminant to be positive. Once again, find the determinant of the quadratic 27k²-12k+10 :
- if it has no real root (that is to say the discriminant is < 0), then it is always positive, which is what you want
- if the discriminant is = 0, then it is positive (as a square)
- if the discriminant is > 0, it can be either positive or negative (in general)