Question

For what value of k does the equation x2 + k = kx - 8 have:
a) Two distinct real roots
b) real root
c) real root

Answer 1

You want to check the discriminant b^2-4ac. So rearrange into quadratic form, ax^2+bx+c first. Then solve for b^2-4ac. To get 2 distinct roots, the discriminant needs to be greater than 0. To get 1 real root, the discrimant needs to equal 0. And to get no real roots, it needs to be less than 0.

Answer 2

Thank you so much!