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Clavis TMUA Set B Paper 2 · Q6

Paper 2Logic & proof

Consider the following statement (∗)(*) about a real number kk:

(∗)(*) For all real numbers xx, x2+kx+k>0x^2+kx+k>0.

What is the complete set of values of kk for which (∗)(*) is true?

Athere are no such values of kk
B0<k<40<k<4
C0≤k≤40\leq k\leq4
Dk<0k<0 or k>4k>4
Ek≤0k\leq0 or k≥4k\geq4
Fk>0k>0
Gall real values of kk

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