Problem: For what real values of K does x=K2(x−1)(x−2) have real roots?
Answer Choices:
A. none
B. −2<K<1
C. −22<K<22
D. K>1 or K<−2
E. all
Solution:
Since x=K2(x2−3x+2),K2x2−x(3K2+1) +2K2=0.
For x to be a real number the discriminant must be greater than or equal to zero ∴K4+6K2+1⩾0. Thls is true for all values of K.