Date | November 2013 | Marks available | 8 | Reference code | 13N.1.sl.TZ0.7 |
Level | SL only | Paper | 1 | Time zone | TZ0 |
Command term | Find | Question number | 7 | Adapted from | N/A |
Question
The equation x2+(k+2)x+2k=0 has two distinct real roots.
Find the possible values of k.
Markscheme
evidence of discriminant (M1)
eg b2−4ac, Δ=0
correct substitution into discriminant (A1)
eg (k+2)2−4(2k), k2+4k+4−8k
correct discriminant A1
eg k2−4k+4, (k−2)2
recognizing discriminant is positive R1
eg Δ>0, (k+2)2−4(2k)>0
attempt to solve their quadratic in k (M1)
eg factorizing, k=4±√16−162
correct working A1
eg (k−2)2>0, k=2, sketch of positive parabola on the x-axis
correct values A2 N4
eg k∈R and k≠2, R∖2, ]−∞, 2[∪]2, ∞[
[8 marks]
Examiners report
[N/A]