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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     b24ac, Δ=0

correct substitution into discriminant     (A1)

eg     (k+2)24(2k), k2+4k+48k

correct discriminant     A1

eg     k24k+4, (k2)2

recognizing discriminant is positive     R1

eg     Δ>0, (k+2)24(2k)>0

attempt to solve their quadratic in k     (M1)

eg     factorizing, k=4±16162

correct working     A1

eg     (k2)2>0, k=2, sketch of positive parabola on the x-axis

correct values     A2     N4

eg     kR and k2, R2, ], 2[]2, [

[8 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2 - Functions and equations » 2.7 » The discriminant Δ=b24ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots.

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